I don’t know if this helps either of you, but as a separated father of a 4-y-old daughter I can add my own experience: my daughter is the most important thing in my life. Not just on a theoretical/philosophical basis, but on an everyday practical one. Even if she didn’t have the problems she has (which meant I gave up my job to deal with it), I would always put her first and think about her. Imagine I had a gf and we had arranged to go out and my ex called the last moment and told me to take my daughter, I’d take my daughter. I might try and incorporate her in whatever we were doing and keep some balance, but my daughter’s interests would always come first (which may explain why I don’t have a girlfriend). Not sure if this applies to either of the men you’re describing, but their kids will definitely mean a lot to them either way.
Also Mermaid’s bf seems to see his kid far too rarely. (and missjena it’s selfish to wish he doesn’t see his kid as often so that you get more of him, his son needs him more than you do) I don’t know if or how much this bothers him, but it’s certainly not the role I want to play. Of course my case is unique in that I was the main carer before the separation and still live at the family home, whereas my ex was the one that left and can’t take care of children. Usually it’s the other way around.
I wouldn’t worry too much about the constant connection with the ex, because in most cases their relationship can never be fixed, so even if you sometimes feel threatened by her, you shouldn’t. It does however become an issue if you have children with him and he has to share his time, love, and eventually property between your kids and hers. And it may not sound like an issue now, but it has always been an issue with men who made two families (especially if the man is rich). Even worse for all of you if the second marriage also breaks down and he has to share his time, effort and money between two sets of ex wives and children with different mothers. It’s the main reason I don’t want to remarry.
My last gf also had a daughter my daughter’s age, and it was good in the sense that we understood each other. Unfortunately our daughters never accepted each other as sister, and since we had different parenting rules (and also completely different children as a result) the idea of making one family out of two halves never worked. But our own relationship was good while it lasted.
Sometimes you girls will have to be a little more patient and understanding with your boyfriend than normal, and remember not to be antagonistic towards the children or you’ll eventually lose. Once you stop thinking of the child and former wife as a threat, and show a certainty in the relationship (“this guy’s mine no matter what”), you’ll be able to not just offer him the support he needs, but get the most out of your relationship too.