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It is hard to say but I think his violence trumps any negative associated with you living with your mother. You would just let the judge know the reason you live together and make it a positive that she is also a big help to you in caring for the kids.
He is going to do whatever he can to look bad. I am not convinced living with your parent who is ailing would work against you and I explained how you might be able to make it a positive.
Let me know if you still have some questions. I do not blame you for overthinking but you just need to tell the truth and explain your position.