Don't be so afraid to lose something that you lose it. You say you're not giving up, but you are, until you have a plan.
Desperate times call for desperate measures, not plans. Do what you need to do, right now.
If you think she'd file immediately, because you moved back in and "disrespected" her, you can say, "I'm sorry if you feel that way, but I want to be near my children and they deserve to have both of us in their lives. I will do right by my children and abandoning them, just because you want me to move out is not an option. Also, this is my home too, and I will not leave it, and be a burden on others. (Whether your parents are fine with it or not makes no difference.)"