What are her issues with your DD? Does she think she's coddled? Rude and disrespectful? You behave differently when she's around?

Be honest with yourself about what the issues are and how you contribute - once you've done that, if you can honestly say those aren't real issues, then it's on your wife to figure out how to deal for 48 hours.  But unless she's really a difficult person (your wife), it seems there must be something you and your DD can do differently here. 

You are Ok with her kids, she is not OK with yours.  Maybe it is your DD, but maybe it is her.  I would suggest family counseling.

Not enough information on why your wife doen't like DD.  She has to have said why she dreads her visits. 

I think one of the biggest fallacies in SPhood is the idea that because one spouse likes their SKs that the other spouse must like their SKs the same way.

That's just not likely or possible. There are too many factors that play into SK-SP relationships, and factors that play into the roles and dynamics individuals have within a family structure, to make that possible. Even in intact families, it's not abnormal for kids to have different relationships with their parents or for parents to tolerate different things from their kids.

OP, you have two courses of action you can take. If your DW just doesn't like having another person in her house, but is otherwise pleasant and respectful to your DD, I'd let this go. Let them form whatever bond (or lack thereof) that they are going to form. Worry about your own relationships and she can worry about hers. If there is no malice in how your wife acts, leave it alone.

If, however, your wife is being malicious/unkind/rude to DD, OR your wife is coming to you expressing concerns/discomfort with your DD's behavior towards her, THEN you can and should step in. This requires a listen first, react later approach. Don't immediately jump on your wife for being "mean". Talk to her. Find out what happened. Then make a calm determination of the situation.

Teen girls can be nasty, as a PP said. There is always the possibility that she is sending very clear but subtle messages to your wife that DD doesn't like DW and isn't welcome to her. And your DD may lie to you in order to drive a wedge between you and your wife.

Ultimately, if your wife isn't acting in malice but your DD is doing things that make her uncomfortable, even if you allowed them before, you need to make your DD conform to the new normal. Alternatively, your DW needs to ensure the same from her kids in regards to you. If it's important to your wife that everyone eat dinner together, but DD is used to eat in front of the TV, drag her butt to the dining table. If it's important to you that all shoes be put into bedrooms at the end of the night, but DW allowed her kids to leave them wherever, she needs to get on them to put them away in their rooms.

There will be peace in your home when you and DW have a parenting plan based on mutual respect for one another. Both sets of kids will benefit from you and DW presenting a united front even if your individual relationships with the kids differs. The kids need to know that it's not "us vs them" but a hierarchy with you and DW at the top. So long as no one is being mistreated, the wants and desires of you and your wife trump the kids. If that isn't a philosophy you can get behind, then your marriage will fail.

ETA: There is also the possibility that your behavior changes as well, which can cause your wife to be resentful of your DD when she really should be mad at you. But she loves you, and it's easier to find fault in the symptom of the problem if the actual problem is something you like/love.

If your wife tells you that your behavior changes, or you allow DD to behave in a way that is unsuitable, then you have to change your behaviors (just as she would if how she acts is different around her kids in a way that causes you problems).

My husband has a teen daughter and never expects me to do things on my own with her. I was also childless until a couple years ago. 
 

Are you using your wife as a buffer bc being alone with a teen daughter is unnerving? Your wife has 3 teens maybe she wants to be able to read a book when they are gone without being mom'd to death. I hope you don't run out to the garage to do "errands" the whole time your daughter comes to visit every other weekend. 
 

If you are by chance avoiding your own daughter maybe your wife isn't annoyed at her, maybe she is annoyed at you for expecting her to bond and entertain a teen on your small amount of time with her? just a thought

This is an issue my DH and I are dealing with right now.  The difference for me is that the mini step wife on steriods is 27 years old now. It just gets worse as they get older (most of the time I'm guessing)  I don't know why or clearly understand how my DH can't see the difference in his behavior when she is around.  I guess one way to help you understand your wife is to acknowledge the "subtle slight digs" that take place.  They are there for sure - you may not see them or interrupt them the same but it is real from a SM perspective.  My husband will be standing right beside the 27SD and miss the digs and the hurtful remarks.  My DH shrugs them off as being jokes sometimes.  Nope - they are not jokes. There are real meanings behind those statements.  It is all whole different message that is being sent to the SM.  Trust me.  Women are also very territorial as mentioned by futurobrilliante99 above.  Nothing is more hurtful than seeing DH treat his little girl (not little anymore in my situation) as if she has done nothing to cause the friction between SD and SM.  I have experienced so many hurtful things from SD that I too resent it when SD comes to visit.  Just know, there is probably something subtle going on and try and show support to your wife in front of your daughter.  Your wife is just as important as your daughter but the pressure will be on you to show that.  It doesn't mean you love your daughter less - just that your wife is just as important too.  Good Luck.  

Did you select a toxic woman as your wife or .... is your daughter not as tolerable and more of a disruption than you may think she is?

Making your DD feel welcome does not mean that she is not held to the same standards of behavior and performance as any other kids in the home.  Also keep in mind that she is not a full time resident in the home. She is an intermittent visitor.  Does how you engage with her when she is there disrupt the others in the home?

My guess is that reality is somewhere at a mid point.   

IMHO the goal is for your daughter's time in the home to be a non event for everyone involved including your daughter.   She is held to the same standards of behavior as the other kids, she is expected to engage pleasantly and not be a disruption, she treats everyone with respect as they treat her.

I can't stand when my SD's come over....and like your wife...it's even worse when my bio kids aren't there and its just SD's.

My DH acts like he is their maid and servant....he doesn't make them do anything to help out...no chores no nothing. They are teens/pre-teens........he will do any and everything they ask...drive them all over town and back again b/c they want to..buy them whatever. No discipline at all....bad grades? Who cares? Talk back? No biggie....we don't want to upset step kids poor little precious feelings...b/c they are so so fragile...poor babies....DH allows his kids to use MY/OUR bathroom and shower when they have their own....oh the list goes on and on.....I dread their presence in my home which causes me to feel trapped, stressed, suffocated, out of place....and makes my DH act like a totally different person.

OP, don't expect much to change if you do any of the things I've mentioned.

"I know my wife is not happy but I need to make my DD feel welcome." You've answered your own question. It sounds like you make a fuss about your DD when she arrives, giving her affection, making her feel special etc. You are unwittingly excluding your wife, making her feel second best and elevating the DD above your wife in importance as though the rest of time (when DD is not there) doesn't matter as much. It is easier to bond with people when you don't resent them. Step it down a notch and include your wife when DD arrives, if the other kids have chores make sure she does too etc just like all the family members. However kudos to you for trying to fix the problem, it takes a real man to identify problems and make a change.

hand in it. You can, in no way expect her to love the child you sired, just because you love her. It's not a pre-requisite to loving you or being your partner.

In all honesty, most of the SM's I have had the privilege of visiting with on this topic, and having been in these shoes myself, I will tell you my DH (and many others on here) turn into a completely DIFFERENT person around "their kids." When DH's very adult (middle aged) offspring show up, I am nowhere on the radar. At first, I thought, "Well, if it makes DH happy, it makes me happy." I would dive in and cook, clean, make beds, wash sheets, everything.Without so much as a simple "thank you." I was reduced to unpaid maid status.  Then I started to notice how my kids (way younger than DH's) would strip the sheets, put them in the washer and put fresh sheets on the beds they had slept in. These are grown young men, mind you. Note : The key difference here is EXPECTATION, and HOW THEY WERE RAISED. DH's kids who are a great deal older than mine are entitled, and they expect the red carpet treatment. I put my foot down and refused to do any of it any longer. He just gets this dreamy stupor on his face when they come around. I'm sure you, unbeknownst to yourself, do the same thing, much to your lady's dismay. Take inventory on your behavior when your daughter is around. Ask yourself how you would feel if she did the same thing with her kids, and how youwould feel. 

If you see she is unhappy and think your DD is the source of it, it's YOUR JOB TO ADDRESS THE BEHAVIORS demonstrated by YOUR daughter. All too familiar is the story of the divorced daaadddeee who will NOT STAND up to his kids and for his marriage. Guess what happens? People split up or divorce because no SO, DW or DH likes being last in their relationship or marriage.

I just suggested it to someone else so I will suggest it to you: read step monster by wednesday martin. Hopefully it will give you some perspective. 

It is great that you are here seeking advice, most men just bury their heads in the sand. As for your wife, she is preserving her sanity and health by staying out of your sd's way. You do not necessarily have to understand her reasons why but just accept that not everyone you love will get on with each other. You are the lucky exception to get on well with your step kids.

There have been some great suggestions above for things to think about but the most important thing to do is to support your wife in her decisions and ask her what you can do to help her feel more comfortable and make sure to really listen to her answers without getting defensive. When you are ready commit to making some changes and make sure that your actions are consistent (keeping it up for a month or so before lapsing will just bring you back to where you started).

Welp I guess we know the OP's DW had her reasons of not being a fan. He's over at Circle of moms now (eyeroll).

Just dropped into COMs.   
 

I have no words.

smh

‘Trying to make everyone happy’ generally doesn’t work for a lot of people. 

I fear this is the fatal flaw in your plan. 

This sounds a lot like me and my situation, except you didn't mention anything about what your daughter is like or why your wife says she's unnerved.

I will be completely honest with you. When my husband and I got together, he babied and coddled his youngest like crazy. I mean, she was 8 years old and he was still feeding her off of baby plates. She didn't do ANY chores and had almost no consequences for several years. She is around the same age as the other two children but was being treated way differently.

My biggest issue wasn't with his daughter, it was 1) how he treated his daughter, and 2) how he reacted to ME when I said something about it.

That created a lot of resentment in me towards both of them.

I just recently started therapy, in part to deal with that resentment. I'm hopeful.