It is about her partner not having clear boundaries of what is acceptable and what isn’t
But it's only OP who want clear boundaries. There is no rule that say that couple who separate have to have clear boundaries. Some people separate and never ever want anything to do with each other, burn every pictures, and break contact with common friends. Others remain good friends. Some break contact with their ex but remain in very close contact with the family of their ex.
Of course, as a new partner, it's much easier to deal with an ex who is completely out of the picture, but it doesn't have to be that way.
I don't agree that because you commit to someone, you have to obligatory stop a friendship with an ex, especially when that commitment is not yet at the stage of sharing a household.
Whether it is acceptable depends on a number of factors. As OP ever worried that there were still feelings for each other. Have there been any signs that one of the two would wish to get back. How do they act when they are together, like exes or like friends. Have they gone away on holiday before and if so what was the set-up, ie, did they spend all their time together etc...
Ultimately, it sounds like he hasn't agreed yet, so it is unclear whether it is something he really wants to do but doesn't want it to cost his relationship with OP, or is he waiting to find a way to his kids and ex that it's something he doesn't really want to do.