While it's great that you are getting out of the "difficult" situation with living in your parents house, I'm just sorry you do not have the support from your mother that you should have. I hope someday you will get that from her. I do not know what I would do without my mom, even though I do not talk to her everyday.
Do you think that not living there your relationship with her will be any different? For your sake, I hope so. Yeah, they will be upset and angry about you moving, but they will just have to get over it. You are an adult and can (and will) make your own decisions. Hopefully someday they will realize that.
I am so happy for you that you will soon be reunited with your furkids.