My guess is that once she has the baby he will go away.
She's only looking attractive to him because he can't impregnate her.
Not to say your wife isn't hot, but predators, as you know, are quick to move in on women when there is small risk and also when they might be feeling vulnerable about their looks (some guys think that women only want to be thin and model-like and are incapable of feeling attractive when they're pregnant, which is absolutely wrong). I agree with others that your W needs some training on how to establish boundaries with men or other people who are unwanted or only partially wanted with limits, in her life. Some assertiveness training would be good for her. If a guy told me I was being clingy if I were sitting with my H, I'd tell him point blank he was being jealous if not inappropriate. This guy is probably justifying his behavior by your past, thinking he is doing her a favor, or trying to convince himself of that. She really has to establish her own boundaries and you can tell her that it is important to you that she does so. If you try to do it, it will be a losing battle, it will only encourage the guy to think that you are controlling and posessive and jealous and that your marriage might be insecure.
I'd make it clear too that he wasn't to visit your W in the hospital if that's where she's going to give birth, she can take care of this by filling out some simple forms that hospitals are required to offer all patients, and asking the nurses in the maternity area to be aware that he is on a no-visit, no-call list.
He sounds kind of creepy. The alternative is that he has a mommy complex, and feels like he is in need of a mommy figure in his life.
When I was young and pregnant there was an embassy marine that had me as a fixture, well somewhere between a mommy fixture in a strange country under martial law, and a crush. But I was aware of it and managed it better. There are some things that are cute, and some things that are creepy. Your wife has to follow her own instinct and not use you as a barricade or go-to-guy for her protection.