I too have a severely overly dominating MIL and I feel your pain! We are living with my in laws for similar reasons as you and I am about ready to move into our camp tent. I too have to clean up after everyone or I get yelled at for not pulling my weight. I also get accused of doing nothing because I work a job that has non traditional hours so they never see me get up at the crack of dawn to go to work. They see me "sleeping in" (never mind I didn't get to go to bed until 1-2am). I have also felt the pain of the holidays and lack of inclusion especially since my family lives on the other side of the country. But the worst is that my sister in law (who is the favorite "do no wrong" child over my DH) had the first grandchild (my MIL acted like it was the second coming of Christ) and since we don't have our first yet, my SIL got to decide how I spent my holiday this year.
We are still in the process of TTC our first child so she isn't doing anything to kids yet, but my SIL had to yell at her several times to get her to back off of sicking her nose into the raising of my nephew. And she treats my DH like he's 15 and has tried to muscle me out of my wife job for our entire marriage. My MIL doesn't comprehend someone asking nicely but she breaks into tears at the drop of a hat making you feel like the bad guy for yelling at her to let you take care of your own family. For this reason, my SIL has all but cut them out of her family's life altogether and honestly my DH and I are convinced as soon as we move out we will have to as well.
It took my DH a long time to understand what my MIL was doing and how it made me feel, I was even considering moving 3,000 miles away and in with my mom. But now that he does understand, he backs me up and stands up to his parents as much as he can. I can't tell you how much better I have felt just knowing it's me and him against them instead of me feeling like I had come in and ruined their perfect family. Honestly I'm not sure if there is much else to be done until you move out. You can say something, but you do risk making a tough situation much worse. We feel like we can't say much of anything because they are letting us live there and they can choose to discontinue that arrangement. I can tell you that her behavior probably won't get any better even when you do move out.
What we have done for Christmas is put up a tree in our bedroom and put all our presents for me and my DH under it and before we leave for anywhere else or go into the main part of the house we sit on the floor and do our own Christmas in their before they even know we're up. We went to our own Church's eve service and if they had some tradition planned when we had planned ours we just apologized that we couldn't make it to their thing and did our thing.
As far as the kids Birthdays are concerned, something my SIL has done is to preempt her mother as much as possible. Example being, she has let her mom know before her mom has a chance to plan anything when the birthday party will be and where and that she is welcome to come at the time the party is set to start and no she doesn't need to bring anything other than a present, the cake is already ordered. She will even give her an invitation. She has her own home so that is easier for her to do, but maybe there is a friend who would let you "borrow" their house so that she has to go somewhere and can't butt in as easy. No one solution is going to work for everyone so I don't know if any of this is helpful, but Big

You're not alone!