Do I stay or go?

I’ve been with my husband for a good three, almost four years now. And recently (a little over a month ago) we had a child together. This is my first and will be my only biological child. My husband has 3 kids with his ex girlfriend who he has been with since he was in high school, roughly 12-13 years together. I am his only long term relationship outside of that. I was married once before him and left because it had been abusive. I didn’t meet his kids until we were living together and had been together for a year and a half. When I first met them, we all got along great. His oldest is super smart and funny. I enjoy that we both love playing video games which gives us something to talk about. He’s 12, almost 13. His youngest is the same and he’s 7 almost 8. I really have no problems with either of the boys, and I didn’t used to have a problem with his daughter until the last year. In the last year, she and I went from being super close to me and her constantly fighting. She is 8, almost 9 years old and up until my daughter was born last month, was the only girl grandchild and child so she had been heavily spoiled. Shes never really told no and has no consequences for any actions. I know she physically beats up on her mom to get her way, often. Her mom does her homework for her and cleans her room for her and allows her to do whatever she wants. I don’t do those things which is what caused us to start fighting initially. It all really started one night during summer when I told her she had to stay in her room until it was clean so she smashed her TV. My husband tried to buy her a new one and I wouldn’t allow him to which made him mad at me. Her mom got tired of me saying she couldn’t have a TV so she got her a kindle fire to watch YouTube on and then my husband gave her an IPad. Effectively negating my punishment for her. She also LOVES babies. So much so that when it came down to me being pregnant and having my baby, all anyone would talk about it how happy it must have made her. They even tried to get her a sash and tiara for my baby shower that said ‘big sister’ even though she is already a big sister. I asked my husband not to bring her to the party because I knew she’d try to make stuff about herself and others would make stuff about her. Which is exactly what happened. Thankfully they didn’t get her the sash and tiara, but she kept trying to be in my lap and open all the presents for the baby and would continuously ask for all of the babies stuff for her own babies. My husband was convinced that I was jealous of his daughter because I got so upset about it all, when really I just don’t want my baby seen as a toy for her. Really everything came to a head THE DAY that my daughter came home from the hospital. I asked him not to bring the kids over because I wanted time to bond with her and get acclimated to being home. He ignored me, talking about how he wanted them there. But, and this has been a big problem since I first met them, he always brings them over and then I end up watching them and doing everything for them while he goes and does whatever he wants. So I really didn’t want them to come over because I was already overwhelmed having not slept in 4 days and being around my very first baby. When they came over, I was breast feeding her and told them they couldn’t come in until I was done. His daughter threw a hissy fit and got mad because I was feeding her and not letting her hold her. Then, the following day when my baby was 3 days old, his daughter started coughing and sneezing. I told her she wasn’t allowed to hold the baby until the cough and sneeze had been cleared up for at least 24 hours. This set her and my husband off. Both of them screaming about how I hate her and don’t want her to have anything to do with the baby. When really I’m trying to keep her from getting RSV. The fight went on for hours with him screaming about how I don’t care about his daughter and RSV isn’t a thing and I should just let her hold her. I held my ground and still haven’t let her hold her if she’s coughing. While he’s adjusted to that and knows better than to fight me over it because he won’t win, he still gets pissed anytime I tell her no because she is generally always sick with something. I was willing to get past this, seeing it as him being a protective dad of his daughter’s feelings, until I told him I wasn’t coming to the family dinner at his grandmas the other night. RSV has sky rocketed in my location. Over 90% of illness here is currently RSV and my baby already has pink eye. I told him we were going to stay home. While to my face he acted like that was fine, I was told that while at the family dinner, his family yelled and screamed at each other about how I’m being too protective of her and she needs germs. During this, he called me fat several times (I am actually smaller than when I got pregnant.) he also told them I wasn’t a good mom because I wasn’t parenting her like his ex parented his kids and bashed me for not being able to feed her enough breast milk. I was already super sensitive about that subject in general which he knew because I’ve been trying everything in the book to boost my supply to no avail. He doesn’t know I know everything he said that night, and of course there are a lot of other horrible things he has said and done, and I’m tired of feeling so broken and hurt by him and not feeling loved. I hate that I know he talks so harshly of me behind my back. I’ve done everything I can to be a good parent to his kids. Both of the small ones neither knew how to read or write or even spell their names when they met me the year before last and I taught them. The youngest can barely speak coherently and I’ve tried to get him into speech therapy but his bio mom won’t let me. His poor ankles nearly touched the ground when he walked and after months of fighting my husband to fight his BM to take the youngest to a doctor, he finally got braces for his feet. Which she doesn’t force him to wear despite doctor orders. I love these kids, and I don’t hate his daughter, but our relationship is very broken because of it all. To the point I dread when she comes over because I don’t want to fight. I try to avoid being around her at this point. I can’t afford to live on my own and pay for child care in my city. My mom has offered me to come move in with her, but she is 9 hours away and this would effectively take my baby from her family here which I don’t want to do. Would I be a horrible mom if I did? I know I can’t trust him to watch her because he always passes her off to someone and doesn’t follow any of her care instructions when he has her. 20 minutes into him holding her and her crying he’s coming and getting me out of the shower and saying he wants to just lock her in the basement. I know how hard he fought for his kids with his ex. But it feels like mine is just a burden on him and she will always come second to them and that I will never measure up to his ex in his eyes.