In my opinion, this is a multifaceted problem.

1st - It sounds to me like you've got a rat in the woodwork. The more you guys are around this cousin-type guy, the more of an issue it sounds like he'll become. Social media is another place his kind likes to troll.

2nd - It sounds like your wife has no leftover feelings for him so that's not an issue. However, it does sound like she's not understanding how guys think so she's being naive about his intentions.

3rd - The difference between what you are perceiving and what she is perceiving is causing friction in your relationship. Grandma, aunts, 4th nieces twice removed can be da$#ed because you guys need to nurture and protect your relationship first and foremost. I would suggest couples' counseling to help you both get on the same page with this cousin before the situation becomes unmanageable. Again, an uncle can go jump off a bridge if it's causing you guys problems in your marriage, so you guys should take a break from cousin until you can work out things between you.