Perhaps instead of getting locks for the doors, you can get those little wedges that people use to keep doors open. Instead of keeping the door open, use the wedge on your side when you are inside. The door won't have a lock on it, but it will be very difficult to open from outside.

Sorry you are having to deal with this. Your mother sounds quite toxic. I disassociated from my parents about 6-8 months ago. Good luck and I hope things improve soon!