Resenting SD, want the CO to change

I’ve been in my SD(9) life since she was about 18 months old. Me her and her dad moved into an apartment just before she turned 3. Bm has been alienating her from us since then and it’s caused such a breakdown in our relationship with her that I feel she is not able to thrive here with us. It was like a switch flipped, a once confident child is not struck with insecurity because her mom is telling her that her father and I don’t love her. When I got pregnant, the alienation got worse, when we got engaged, married, same thing. Just a constant battle having to reassure SD every time she comes home parroting her mother’s words. My husband has primary custody since she was 3, bm gets her Eow plus 2 hours every Thursday, and she is relentless about dividing her from us. I always told myself that I don’t have a problem with my SD even though the resulting behavior is stressful, it’s her mother that’s creating this, but now after 7 years of this I am completely burnt. I have a 4yo daughter with my husband, myself and my daughter are taking the brunt of this dysfunction. My BD(4) is very sweet and loves her sister, always thinks of her even when she’s not around, shares with her unprompted, defends her etc, but she gets the exact opposite treatment from her sister. It is to the point now where my daughter can’t even talk without her sister talking over her and being annoyed that she’s talking. Anything my child does she’s being yelled at, called names, hit etc. I asked my husband to take more of a responsibility when it comes to these behaviors because most of the time it falls on me, and he has tried, but there’s only so much he can do because I’m at home most of the time and he works, there’s a lot of times where it’s just me and the girls, and she acts up more when it’s just me because I’m the point of contention for her. The last straw for me was a few days ago when my mother in law was visiting, she was going to stay the night but decided not to. SD begs and begs to go to her house with her and spend the night. MIL said no, I said “no Bella it’s a school night and you have to do your night routine and get ready for bed”. She still begs regardless and says “please grandma, op needs a break from me” cue record scratch. Now MIL is looking at me with a raised eyebrow and asking SD why she said that. I say “idk, her dad did have to talk to her about her behavior today so maybe she’s talking about that”. SD continues to beg and MIL asks her again and she says “oh I was just saying that so you would take me”-.- ok girl you’re just going to start problems for me so you can get what you want? Got it. She still not taking no for an answer though she’s been told plenty. She even gets in between her grandma and the door and locks all the locks back. So I just snapped and told her very firmly it’s not happening and it especially won’t happen cause you beg. That wasn’t even the worst part. I task her to do her night routine and as she’s walking across the livingroom her sister(4) tries to talk to her and she instantly starts obnoxiously yelling to tune her out, then when my kid finally gets a word in she turns to her, rolls her eyes and says “ugh what do you want?”. I call her in my room and I ask her why does she think I’ve called her. She tells me exactly what happened, so she’s aware. Then she tries to make excuses for acting like that, I tell her I’m not interested in hearing the excuses and she starts yelling at me “ITS NOT AN EXCUE ITS NOT!!!” So I just send her to bed early. Upon realizing she actually has to sit with her consequences she throws a temper tantrum, like a full grown toddler. Screaming at the top of her lungs. I tried to go in to talk to her but she kept screaming at me so I left and then she was like “wait!” But I stayed gone and so she just kept screaming. I called her dad and let him talk to her. He was trying to make it easier for her which honestly pmo cause that’s part of the reason why she doesn’t take consequences seriously, but in the end he let her stick with her punishment exactly how it was given to her. To make matters worse, when SD was screeching, it was making my 4yo so uncomfortable that she asked to go to bed early too to help her feel better, when I told her no, she said “but it’s ok, I love her”. So here my child is learning to accept mistreatment just because she loves the person doing it. It broke me fr and I was already hanging on by the littlest thread. This is one of many incidents that have this same theme. Me and my child are constant expected to absorb this behavior and I’m expected to be accountable for fixing the fallout of it. My therapist and MIL asked me one day about a month ago “why can’t she just stay with her mom?” And I was opposed to it at first because she’s already learning poor behavior from her mother but since they asked I’ve been entertaining the change in my mind and I honestly think it’s for best. I’ve talked to my husband about it and he thinks it’s probably for the best too but he’s scared of the effect it will have on SD. She wants to live with her mom too, and I think it will be best if she lives somewhere she doesn’t have to constantly scan for equality and live in comparison mode. I don’t think she’s able to thrive here and honestly I can’t sit by and watch my child get bullied everyday and learn to take abuse. I’m scared tbh. I’m scared I’m going to have to leave my husband and I’m scared he might leave me. I really need to hear something from people in similar situations or any guidance at all really.