Well, right now, that convo would be rife with emotion. I think you just have to trust H at this point and not obsess about the what if.

And if he did meet her at park, but didn't tell kids who she is, well, kids are not stupid.

I think you should have this conversation with H. I did. He told me that GF and he were in serious relationship. I said it was time to tell kids about her, but that his time with kids was his time, not plus GF time. For now, anyway. I will not have a series of GFs introduced to D. If he should break up and re engage in another R with someone else, I will refuse to have her introduced until a year minimum goes by...all I need is a parade in my kids' lives.

But this is something you will have to address for your own peace of mind.