These children are only with you 2 days at a time. There is only enough time for them to settle in and they are off again. No they should not be on their cell phones all the time but this is the nature of the beast in this century. In a few years it may revert something else. 

As far as the influence towards your children ... honestly with the amount of work you put into yours do you really think they will flip so easily into Skid-Mode? You say they are gifted yet you do not credit them with any intelligence to make good choices. Ease up on your kids. They will have to face lots of conflict and negative personalities and just downright mean people in the big wide world, Better they learn to handle this kind of thing now with you there to guide them back into acceptable behaviour rather than having to deal with ths later when they have a shitty roommate.

I would not write anything to Miss12. You may want to talk to her though. "Miss12, I know I am not your mother and I would never want to be your mother because you already have one. Who needs 2 mothers? But if you have any problems or things you want to talk about, I am here. Your Dad is a man and has no clue what goes on in a womans brain. I have been a 12 yr old girl and know the score. Whether you decide to talk or not is entirely up to you, just saying the door is open. Speaking of which would you please help me take your laundry downstairs? Thanks."

Baby steps. They change houses every few days, I presume your kids are yours and DHs so they never ever have to go anywhere. Your Skids have different parents and yes, you knew this going in. I know people get angry about this but you knew the parenting your DH is capable of and married him then had 4 kids (I assume) and want the whole house to run the way you want it irregardless of how these skids were previously raised. Sadly as 2nd wives we do not get the option. If we want that option we should not marry a man/ woman who already has children.

You have permission not to love your skids. You don't even have to like them. You are expected to abide by the law and not cause them any harm. But if you want this to work out somewhat (and DH can deal with this son) start by saying hello when they walk in and smile at them. Remind DH this is a 2 way street and agknowledging your greeting even with a glance and 'hi' would be a start. Walk up to their rooms and knock on the door and say "Dinner is in 5 minutes." If they are fighting use your outside voice and tell them to "Hey! Knock it off! If you want to fight AGAIN take it outside." Then open the door and point. Redirect their behaviour away from your kids.

They don't sound like the worst kids in the world and as they are in their teens ... well lets say your kids aren't even there yet so they may surprise you with their own tricks. You can do all the focussing you want on their education and wellbeing but once those hormones start rousing themselves, yikes!

And no, I do not love my stepsons as my own although my DH loves my kids like his own. I don;t make it known and he would probably be surprised at me ( a have good acting skills). But I am more like an aunt, the fun aunt, As in your case my skids already have a mother and I do not need another 2 sons!

Maybe you are taking this too personally.  My SD has done this many many times before, and I really think it’s just a way to manipulate her dad into feeling sorry for her.  When dad feels sorry for her she gets behavior passes, stuff, and dining out trips

My SD15 has said the same thing about not feeling welcome here and I can understand her perspective. I know that I was not engaged for a period of time. I was really struggling with her dad not addressing some of her behavior and a lack of expectations and boundaries. I felt like I didn't have any control in my home, and it led me to get treatment for depression.  So for a while I was just struggling to maintain and stay here, while she probably felt it as I didn't want her here. Which is not untrue.  When she was here, which was 50/50, she ruled the roost.  If she wanted something, DH hopped to do it, she was disrespectful and flat out refused to clean up after herself, and he didn't force anything.  I would make my requests of him for my expectations (which were minimal), and he would come back at me for it.  So yes, a lot of resentment built up, and I am sure she could feel it even though I have never said anything.  I just tend to pull into myself.  DH and I ended up going to counseling which helped us a lot.  We both have found ways to improve and see each other's perspectives. SD does not come over very often anymore, which is kind of normal at her age I think, but when she does I make an effort to engage with her.  We are not BFFs, but I think things are better than they were. DH had become better about not catering to her, and while that has caused her to pull away at times and play the "you don't want me" card, he is consistent with reaching out to her and eventually she comes back around.  I have thought about writing a letter or talking to my SD also, but I haven't found the right moment yet.  I feel like it could never hurt to let someone know you love them, but I don't want it to turn into talking about why I pulled away, I feel like that would end up making things worse  So for now I am going to keep taking things day by day and trying to stay open with a positive attitude.  I totally understand where you are coming from, and that it is a hard place to be.  I think most of us go into marriage with someone who has kids with intentions of building a loving relationship with their kids, but there are so many complicated factors that we would not even think of.  I am thankful tobhave a site like this to be able to share our experiences