If your wife is confident in herself and in your love for her, I don't see what's wrong with the emailing. Although if I was the wife, being human, I would be insecure, I would be giving him extra attention and loving just so he doesn't get any ideas or deviate from staying on track and honoring his marriage vows. I'd stay secure if I was in love with him and he was with me.
I would pray he sticks around and stays faithful but only Allah knows what's in store for you three. But ignoring the ex friend might be cruel since she might have been there for you when you needed someone to talk to.
If your ex was your friend first and she was darn good one, then I don't see why the friendship can't stick.
I don't have a problem if they're still FB friends, occasional Salam Dua, Eid Mubarak messages etc. and certainly don't mind if she is contacting for professional reasons like job advice or advice on moving to a new city etc.
So if it's casual stuff then fine. You know people have had crushes on cousins I'm sure and we end up keeping in touch with those cousins, and their new families, so I don't see it as a big deal.
I'm friends with a number of women who are married to guys I used to have crushes on in the community. Is there some awkwardness? Maybe. But I end up keeping in touch with the guys wife and I love seeing their babies. Old feelings are in the past, they are dead. Out of respect for the guys' wife I don't communicate much with the guy, just mostly with the wife.
Although, I don't think the ex should keep in touch with the husband for her sake. If she's only seeking friendship with absolutely no sign of those feelings at all from her side(rare), great, I still go with what i've said above, but since you said there were loving feelings before, she might be hurting herself by keeping in touch with the husband because she isn't moving on or finding someone for herself that is readily available because keeping in touch is a constant reminder of how he hurt her by marrying someone else. Keeping the friendship alive, from her side, is not worth it, I say screw the friendship with the husband, the ex is fabulous, she shouldn't keep in touch.......just sayin
I would be irritated. The response, if any that the person should get is to basically bug off if they don't stop. I think old flames have a place in your life and that's in the past. When your married or getting married, I don't see why old friendships that were potentially more than just that shouldn't all be left behind. If somebody feels the need to stay in touch because they don't want to let go of something or look bad then that's a bit of an issue in my opinion. Just don't respond or respond with something that makes it clear that the communication isn't wanted, without any drama of course. It's just the loyal thing to do.