Right now a lot of people can say that you've just had baby, you're stressed, you're overly emotional because your hormones are still all over the place, you shouldn't be making rash decisions. All that is true. But you're not being dramatic. Or a bitch. If after 9 years your partner can throw you under the bus when you're at your most vulnerable then what kind of a partner is he?! It's useless and too late to say "oh i should've never married him" or "oh I shouldn't have had a baby with him". But it's not too late to decide what to do next. Would he agree to counselling? If you left him would he even try to salvage the relationship or just not care? More importantly, what do you want to do? Have a long hard think about where you want to be this time next year. And then make the little steps to start to bring that plan into action. 

You are not wrong, not being dramatic & you're not being a b$)&@. I have had faced the similar things. When reading it in your post, I realized that I have let myself become very unhappy for the second and last time/marriage. Divorce seems on reasonable & required for your happiness, peace, respect & sanity or at least, that is going to be my approach. I have been used & disrespected for far too long.

First, all your instincts and feelings on this are all entirely valid.  Most of us have lived this same scenario.  But you just had a baby, and you are probably physically and emotionally drained.  I believe you need to get more rest and help and try to work this out before you even think about leaving or divorce.  If you get divorced now you will still have to deal with your DH for 18 plus more years (and maybe his Skids) and have the hard life of a single mom and joint custody with back and forth.  It's easier to try to fix this situation now.

It sounds like you need some help at home.  Can your mom come stay with you for awhile?  Can you go back there to stay with your mom for more frequent visits to take a break from DH and Skids?   Can you hire a cleaning person 2/3 times a month to help with all the big deep cleaning?   Also, can you hire a college student-type babysitter and go out with your friends to get some "you" time.   This will all help with your overall stress levels and let you have more patience.   
 

Then I would immediately schedule a marriage counseling session with a recommended therapist. Have this therapist help you explain to your DH that you have reached a potential breaking point with him and your Skids and need professional help.  Tell him you feel he's not being respectful or supportive with your concerns about his Skids and their not pulling their weight in the house.  These kids should have a few daily household chores. (I always insisted my 3 boys take turns, unloading  dishwasher every day, helping clean kitchen after dinner, and take out garbage and recycling, as well as make their bed (they didn't always do the beds). But now my kids are 17 and 20s and they are all 3 great at cleaning kitchen and helping with house because I required it as part of being in family. They also had to rake leaves, and shovel snow, etc.  Kids will do what they are told if you ask nicely, explain that you are a family team and everyone needs to do their fair share   Kids understand about fairness.   But your  DH needs to help with cleaning too or they won't.  I also had my husband helping with cooking and dishes so my sons had a good role model.  Everyone needs to have chores and work as team. Do not do everything like their maid OR they will let you!  No one "likes" cleaning but it must be learned and done!

Remind DH that these are "HIS" kids - not yours and so he's actually the main one in charge of making sure they have a good role model, that they follow house rules, behave, and clean up after themselves.  Remind him you are not their mom or their maid.  Get him to rethink his job as their dad quickly.  He brought them into Your life not vice versa so he needs to be more of a leader. 
 

I really wish I had done this much earlier with my DH and my own SD (who only visited 3/4 times a year) because he also would "blame me" when he talked to my SD about needing her to follow house rules.  She was older and treated much differently than my own 3 sons.  She would ignore me unless he backed me up.  Often he would also "throw me under the bus" like your husband did by blaming me for any requests -- so that he didn't look bad.  He also didn't care as much as I did about all those household cleaning rules.  I was the primary enforcer.  Sounds like your DH is the same.  That's obvious from how your house was when you returned from trip to your mom's.   He didn't clean at all!
 

So you need to be very clear that you need a clean house and floor for your new baby to be happy -- and your Skids and DH better raise their cleaning game.  Too bad if that inconviences them.  Be the leader on this and ignore the balking.  Type out and post a list of weekly chores for Skids (and yourself and DH).  
 

But important to Talk about all this in marriage counseling and have a neutral 3rd party therapist help you explain all this to DH why it's so important.  Sometimes spouses listen more to a therapist saying it.  
 

I would do all this for at least 1-2 years before I even thought about leaving.  You owe this to your sweet new baby.  I promise you can change your household if you have the confidence that you are the real leader in the house.  But be kind and polite with your requests - just VERY firm.  Everyone will end up respecting you even more if there is order, clean,  and calm in the house!  Good luck and big hug!!

You've given it NINE years. That's plenty. Your SO clearly doesn't care about your feelings or needs. 

When we first get with a divorced person they usually gibe us a reason for their divorce. However the longer we spend with them the more we begin to understand what that real reason was. Your husband has not grown beyond playing the blame game. He's so afraid of being the bad guy that he would throw you under the bus for completely reasonable requests. I don't understand what goes through some people's heads when their partners ask and then begin to nag and bitch about normal household tasks. These things need to be done so what makes them immune from doing it especially if you have a 9 month old that you need to watch. I'm pregnant and I have a 10 month old so I know what it feels like to be exhausted but have to give all of your focus to a baby. My husband jokes that I have become lazy but he steps up to make dinner do dishes and other chores. Basically one of us has to watch the baby while the other get something done. One person can't do everything and it is ridiculously selfish of your husband 2 at like you are being unreasonable for wanting the dishes cleaned.

I'm not sure why but these types of men seem to think that their relationships with their children are conditional and they need to walk on eggshells to constantly please them and never asked anything difficult of them. Meanwhile they treat their wives like their love is unconditional even though they've been divorced already so they should know it isn't.