She does not try this with your father because he ignores her and treats her as a leader, and like the dog she is.
Frankly, I do not think she is wired right. It is one thing to bite out of fear or being startled, but it is another to show teeth, bite, and maul the person who lives with you and feeds you, and cares for you.
It does not sound like this is a new behavior, like she has suddenly developed rage syndrome or epilepsy or a reaction to medication, or even a brain tumor. It does sound like she sees your mom as more of an equal or even below her, and when she bends over her to "kiss" her, the dog is seeing that as a dominant-aggressiveness on her part.
Kissing a sleeping dog is crazy. Have you looked at the size of those mandibles? Do you like to be awakened by someone kissing you? If you do, then it still doesn't mean that ANY animal would like this.
Be that as it may be. I think your dad is right and this dog has done too much damage to be a family pet. I think you are right that sending it to a pound means euthanasia. Far too many friendly dogs are euthanized each year just for space, that keeping an animal that will cause medical bills to the people that will get it from the pound or shelter doesn't make sense. It gives a bad name to shelter dogs. And the right person will sue.
You've raised the dog for six years, the problem is yours. Either you find someone very experienced with GSDs who is looking for a project, with full disclosure. Or you find an excellent trainer and all members of the family are willing and able to follow all advice from the trainer. Or, as hard as it is, you make that visit to the vet and put her down, so that she does not bite anyone else.
I am sorry you are having this trouble. Maybe you can fix it. I would definitely try to find a good trainer. But rehoming her, I wouldn't do.
Bear Cub, Hepsi-Pepsi
Cujo2, Karma Chameleon
Ramona the Pest, Kojak -- who loves you baby?
Tiny Tinnie, Susie's Uzzi, Kaiah -- The Baby Monster.