Custody Problems

My cousin has a teenage son with Aspergers. Her and her husband have been separated since he was in the 4th grade and officially divorced last year. She currently has full custody of him and he visits his dad a few times a year. His father is in the military and is currently living in California. He has not been a great father over the years and was a horrible husband to my cousin. He mentally abused her and cheated on her with one of her friends. He hasn't really ever taken care of his son and had a hard time dealing with him when he was younger due to him being more difficult due to his Aspergers. I feel like that sugarcoats it a little so I'll put it a little more bluntly. He's a bad father and really a bad person in general. He hasn't kept his son for more than about 2 weeks at a time since they separated. If it tells you anything about him - his parents sided with my cousin after the separation and sees her more than their own son. Well, he recently got married to a woman that he met online and the first time they met in person is when she moved to California for the wedding. Also, the son found out about his dad getting married ON FACEBOOK and my cousin had to call him and tell him to invite his own son to the wedding. According to her ex-husband (who she has 5 kids with and he has custody of all of them, none of whom speak to her at all) she is a nut job. She's was never physically abusive but has treated all her kids like they pretty much didn't exist after they divorced and he got custody. The son has it in his head that he should live with his dad since he's married. It's just something that he's decided and that's his main reasoning. My question is for anyone who's had to deal with this sort of thing before and if you have any advice. She's so torn up about it because he's her only child but she doesn't want him to resent her if she fights this but she also doesn't want anything bad to happen. The dad and his new wife want to go ahead and change over custody and child support arrangements now which prompts me to believe that they're just wanting money. Advice?