Wow, I am sorry to read this. I don't want to upset you, as it sounds like things are tough, and you seem young. It doesn't sound to me like you are in a position to care for this kitty. I think I would try to find a home for her, where the mom/dad realizes this is possibly a medical issue for the kitty, and, the cut on her tummy needs to be addressed. I am sorry you are in this position. I just don't think you will alter your mom's opinion on this, and I am concerned for the kitty. Maybe you have a friend that your mom likes/trusts, and talk to her about solutions?