Hi
This is a difficult and sensitive issue. I will share my experiences. I am sure all people have different views brought about by theirs.
I take the view that if my kids are away from me there would not be a minute I would not be thinking about them.
I would want to meet my ex's new partner, no matter what the circs of the break up, within reason. They are likely to have to spend some (whether significant or not) time with my kids. You wouldnt send your kids to any old childminder that you had never met, would you?
I say this, actually as a non parent. I can't have my own kids.
My DH's ex was quite happy to drop his kids at the gate for a whole weekend every week with me there and run away like a startled rabbit!! No eye contact, nothing (She left my DH for a neighbour BTW some time before we met). I found this so hard to understand. I had no experience of kids FFS and she knew that, I could have been feeding them Stella and monster munch all weekend, getting their ears peirced, introducing them to Tyson, my pit bull terrier with a short fuse..
I took the bull by the horns and insisted that we met, to talk about the kids and her views about what she expected of me (my DH was there too) for her and the kids' sake, not mine.
We are poles apart on everything (this is putting it mildly) and will never be friends, but we have to accept for better for worse we have a common ground.
I have failed miserably though in persuading my DH to meet his exW's partner..despite the force of my argument with my DH. His exW will have nothing of it and is denial that they are in a relationship..lol.
Sorry if this comes accross as a bit patronising, but it is something that I tried to "man up" about when I realised that my DH and I had a future.