Firstly to all those making out like it wasn't a "serious" relationship or that it wasn't as important/memorable/hard to get over because "they never had sex!" love and sex are 2 completely different things, you can very much be in love and be infatuated with someone without having had sex FFS. It doesn't make it less of a relationship emotionally.
I've had 2 relationships, both long distance because i met both online and didn't live close and illness meant visiting etc wasn't possible. 18-21 was with a right abusive asshole, but got on so well with his mum, had independent friendship with her and when i ditched the parasite i was upset to have to lose contact with his mum. I used to buy her cards and flowers for mothers day etc, and i had lost my own mum. Still i wouldn't ever want to be in contact with or visit her as i have no interest in her son and wouldn't want to know a damn thing about him let alone see him and conversation would inevitably involve him.
Second was 22-25 with the most incredible person i've ever met. We only split up as he started having lots of problems with depression and anxiety and wasn't coping with being in a relationship. Neither have dated anyone else, still love each other 2 years on, and i at least hope to rekindle the relationship at some point, i'm still completely in love with him and honestly think i always will be so tbh i can understand his ex not having moved on, but it does sound very weird that she was so distant and uninterested when they were together as she didn't act like she loved him.
I'd be devastated if he started dating, married and had kids with someone else, but no way in hell would i chase after him, and i honestly wouldn't want to be friends or have contact, i wouldn't want to see him being happy with someone else.
In your position i really would be insisting on him cutting contact, yes it's a shame that they were the only real accepting "parents" he feels he ever had, but they were a package deal that came with their daughter. It's unfair and completely disrespectful to you and your children to keep in contact. He has his own family now, it isn't right for him to put you second to placate an ex or her parents, however close they used to be, as his mum has proven by the picture sending that she can't have a friendship with your son separate of her daughter and trying to rekindle the past.
I would genuinely feel betrayed by him friend requesting his ex, especially knowing via his mum that shes hurt, never moved on etc. Despite it being wrong for the reasons he's married, has a family, etc, it's just cruel to her as it will give her hope (hopefully false) that there's still something there between them or that there are possibilities of getting back together.
It will hurt them as a family of course, but your husband really does need to cut contact, albeit gently, by explaining it's straining and hurting his family (you and kids) for him to be in contact with an ex and ex's family, and he has responsibilities that have to take priority.