My gf (21F) wants to break up with me (23M) over relationship with her parents

My partner and I have been together for a while and we even have an almost 2 year old daughter and our small family going for us. When my daughter was born she said it would be a good idea to live with her parents for a while as she would be more comfortable and have more support for after the birth and everything, I really did not want to live there but to support her and be there for my child I went along.

Jump to last summer , her parents love to drink and sometimes act out of pocket or aggressive when there’s a minor inconvenience. The mother is extremely controlling, has anger issues and can be extremely toxic. One day she decided she’s in a bad mood and takes it then it on everyone, swearing, yelling, scratched my car , wouldn’t let us go when we wanted to leave the situation and had the cops called at some point. An hour later she said that I was disrespectful and many other things because I told her to stop and that my daughter is right there and that she shouldn’t be around this. She told my gf that if she wanted to return home I wasn’t allowed there, that day we spent the night at my moms. I was honestly so angry and disappointed because I liked her as if she was my second mom but after that day I really didn’t have the same respect for her or love , I distanced myself and really broke a branch. Fast forward to later that summer , her, my gf and my daughter went to France for a few weeks , in that period the mom once again got drunk and started talking down on my gf and being disrespectful. After that day we decided to leave and find our own apartment.

Time skip to last week , we go and pick up food my gfs mom made for her. The dad (drunk) starts knocking on the window while we are parked as my baby is sleeping, I tell him hey the baby is sleeping. He continues to say ok have a good day see you tomorrow, I say “yeah you too, see you tomorrow “ we leave and enjoy our family time together when suddenly the mom calls saying the dad is now angry I didn’t say hello , the mom is also angry and saying all kinds of things about me and how I am disrespectful etc, then proceeds to disrespect my gf aswell. She threatened to sell the car we are co owning and that we are paying for because she was annoyed. We use the car to bring my daughter to daycare, for my gf to go to work and soon school again and just everything so we can get around. The mother even said she would take me to court because I didn’t let her see her granddaughter enough ( they go atleast once a week if we aren’t busy) my own mom sees our child less. After a few hours of this none sense and back and forth between everyone the mom finally gives us a break but now she’s being nice with my gf and just like that my gf is all nice again and easy to forgive. On the other hand I am still furious and am still, I told my gf I didn’t want anything to do with her parents and didn’t want to speak to them as I was tired of this nonsense. We got into an argument ourselves on how I shouldn’t talk bad on her parents and to forgive them for a “small” slip up. I refused, don’t want to be involved in something like that and to involve my child in it. Now she is turned against me and on her moms said threatening to break up with me over this since I can’t have a relationship with her parents. I fear mainly because I don’t want to be away from my child, aswell as her being raised in the mother’s house. I was raised in a toxic and abusive home and I wouldn’t want the same for my daughter
Any insight or advice would help thank you!