Frankly, the illogic is brobdingnagian. Why should you have to give the dog to one who abuses you? There is no guaranty the abuse will stop whether or not you give up the dog. Just the same, at the very least the abuse should stop as a condition precedent to even considering giving up the dog.

Your son wants to reconcile. He should be talking to her about stopping the abuse. Since that appears to be unlikely, my thought is for your son to ask her to go to joint counseling with him to work on their issues, including the death of her father. If she agrees to go to joint counseling and the abuse stops, then you might want to consider returning the dog.