I'm not surprised you are tired - a new baby, full time job and looking after your husband's children - the latter of which is most certainly NOT your job - it sounds like your DH is behaving like an extra child rather than a father.  Sorry to say, but I'm afraid you have made a rod for your own back in being so efficient at it all.  Have you shared with DH how much it is getting you down?  The fact that divorce has gone through your mind should make him sit up and take notice, one would hope.  Time for a Come-to-Jesus meeting and don't pull your punches - things need to change in your household to make your life a life, rather than a round of drudgery. If he shows no interest in taking some of the weight off you - either himself or through paid help - then I would suggest you voice the possiblity of going back to separate households. 

Wrong for feeling fed up? Are you kidding me?  I am surprised you have held up for so long. Look, his kids are his responsibility, not yours. When he gets home from work, he does the work - homework, getting them to clean up after themselves, taking a shower, etc. When they ask you for anything, learn to automaticaly respond with "ask your dad" even if he's standing there. 

I can't get past the idea that you were working full-time with SIX kids at home to take care of. Do these people(your husband and his mother) not understand that you were WORKING. Tell your husband to take the six of them to work with him one of these days and see how much work he actually gets done. As for no babysitter, you are going to have to force his hand on that one.

For the time being, the next time he is there at the same time as all of the original six kids, pack up your baby and leave him to it. Spend the weekend with family or friends and get some sleep and try to relax. Do not answer the phone if he calls. Ignore his texts. Before you leave, take time-stamped photos of the house so you can show him that it was in good order when he says it's no messier than when you left. It will also give you some nice before and after photos - who knows what you might need them for?

Next time he says he can't help because he's "exhausted", I'd probably respond with "yes, men are such weaklings..." (no, that is not my personal view of men but only of this "man" who is a bad husband and a pathetic parent) and walk away. How does he imagine YOU feel? Put all of the work for his kids back on his shoulders. If he can't be there with them, either he gets a sitter, takes them to work with him, or he sends them back to their mother. Never forget that these are not your children and therefore not your responsibility.

I don't suppose you get much support from him for the baby either. How old is the baby, by the way?

Are you wrong to be fed up watching 7 children?  three that you did not create? NO.

Now.. my first opinion/reaction was tbh.. that you and he already had 3 kids a piece.. and your primary responsibility should be to them and perhaps getting into another relationship with someone with lots of kids wasn't in everyone's best interest.. and then you did have another child too.. so those are choices you both made.. and they are choices Made.. not really anything you can change at this point.. (I mean.. am I saying that people with kids don't deserve to have new relationships? maybe if they can't sometimes.. the answer is yes if they can't manage their first responsibility of their children as your husband's situation seems to be).

But.. what to do.. what can be done?  He works shift work.. perhaps in a more physically demanding job than a teacher? in the elements?  (just wondering what kind of work?).. he may well be physically spent and off center from shift work impact on sleep etc.. my husband works shifts and it can be exhausting when you aren't getting proper rest.  But. you also have a lot on your plate.. you are going to work now.. and then coming home and keeping the house running and it's so much the norm.. his kids just see you as the default parent to go to for things... when it was 3 kids that had to be a lot.. now with SEVEN? it has to be a ton more!

You need relief and if he can't provide it physically.. then you both need to figure out how to make it happen.  Are any of the kids old enough to start helping out with their siblings.. with the home?  Ideally it would be that the respective bios of each of you could help with their younger bio siblings.. but getting the kids to be pitching in with things vs causing more work for you should be a priority.. since you are the "at the helm" parent.. you should start setting these expectations.  Kids can learn to do laundry.. pick up mess.. cook meals for themselves.. be responsible for their own rooms.. do garden work.. yard work..etc.. you have a potential army at your disposal.. they should be expected to pitch in to the home.. 

You also have a chance to get them in line with behavioral things.. like yelling inside etc.. they learn inside voice. they learn to resolve conflicts amongst themselves.. (my brother and I learned the outcome was MUCH better if our parents didn't get involved..lol).

And.. maybe you  need to take advantage of other things like grocery delivery.. make your DH responsible for some meals.. even if it means his "turn" is takeout or pizza.  Have a cleaning service?  Even looking into after school care for ALL the kids (not just his).. to give you a break.  it will still be a lot.. but maybe it might be somewhat helpful?

I would definitely look to summer camp options.. lowcost options like church camps.. or local daycamps.. to give you a tiny bit of relief.

Do the kids ever go to their mom's?  maybe his custody doesn't need to be what it is? 

I get it though.. with all those kids.. money may well be a limiting factor.  his job may well be a limiting factor.. sure.. if you were not there.. he would have to figure something out.. but that would likely be another wife willing to help him (or would at least accept it)  He may not have a choice with his schedule.. he may not be able to afford daycare.. or camps for his kids.. not without your household income taking a huge hit.  

In the end.. you will have to look for options that you can handle when it all is in balance.  It's easy for people to say.. "make him send them to daycare".. but when you marry.. even when you have separate finances.. the other partner's financial stability and ability does impact your home.  he may not be able to afford those options for his 3 kids.. may not be able to get a better or different job.. getting a 2nd job may not be possible for him.. not with his schedule.. and that would just leave MORE time you have to deal with his kids.

I think you have to be honest that you are getting burnt out.. and ask him for his hellp in figuring out solutions.

I never asked to do this and feel like it isn't fair on his part. I also feel like his mom expects me to do the same... every time I ask why doesn't he find a babysitter it causes conflict.

-----------------You have every right to feel and be fed up.

I'd pack a few days worth of stuff for you and your kids and the baby. Then I would go to your parents. Or siblings. SOME-WHERE

I would not spend a week. You do not want to wear out your welcome.  Maybe just three nights. Tues arrival, return Friday, mid to late afternoon.  :)   You may have to plan a few of these visits until school starts. Possibly during the holidays too.  It's good for the children to have quality time with your parents AND for you too.

You know like summer mini vaca's. No harm in that, right?  Dad can figure out where his and BM's three are going. Maybe he can take them to work. You know like you were expected to do. Fair if fair.

Are you expected to return to work? Full time in the fall? THEN watch all 7 when school is not in session?

JMO of course 

Are you wrong for being fed up with status quo? NOPE

Time for a heart to heart with your partner. Things definitely need to change. And your MIL has absolutely no say so in things - YOU are the queen bee. 

That being said, you really should talk things out with your partner. Lay it all out there. And next time he is home and skids ask for something, defer them to daddy cakes. He doesnt get a free ride here.

No, you are not wrong for feeling fed up.

So, give him full kid duty... half of the evenings.  Every bit of it.

I have no BKs.  I helped raise my SS with my DW.  Usually we both were doing together.  Some times, one or the other of us did it when the other needed a break.

Make sure you get your break.  

My DH and I both had 2 kids a piece when we got married. I tried the "being the mom figure" in our home. After he stopped asking if I would watch the kids and just drive off. I told him NO. If he wasn't there to be with his kids, the kids stayed with BM. If he asked sometimes, I would say yes occassionally. But once SKIDS said to me, they didn't have to listen bc I am not mom. I stopped it all. I made DH take his kids to work with him on weekends.