I'm like her ex. I call my daughter every other day and get her every other weekend or every weekend I'm allowed to. I don't have any problems with who my ex dates as long as my daughter is treated with respect. A few times I had to step in when some chump stepped out of line.
I'll say this...date more women. Let this be a FB or a ONS at best. But don't fall in the trap. I don't know how old you are, but I think you can do better. Leave the single moms alone if you can. It's a reason why she is single, trust me. The ex could probably write a book on it. And be wary of anything she tells you about him, if she starts with the he's awful stories, remember, he loves his kids enough to be there for her, he can't be all bad.