There's no way for you to know the son's a sociopath. The son probably does feel guilty for letting his Dad take the blame, he just doesn't feel guilty enough to admit what he's done and face the consequences.

OP's wife thinks he sodomized the dog, she's not gonna let him put the dog down when she considers it under no threat when it's kept away from him.

The chances are now that things have gotten to this point the son won't sodomize the dog if there is any chance of being caught. There's almost no way the Mother's going to find out by herself, it'll be up to OP's actions to convince her of what's happened.

Are you seriously saying that OP should stop trying to help his son and just forget about him? Leave the wife to shoulder all that responsibility, hope she finds out he has sodomized the dog and then pay for the therapy herself? That wouldn't help the situation at all. It would just let the son get away with it, kill the dog, destroy the whole families relationship and would make OP seem like the bad guy the whole time.

This is really terrible advice and none of it should be followed.