Is there a word for my ex-spouse's new spouse?
Solution 1:
No, there isn't.
This sort of kinship relation is relatively new to Anglophone cultures, and there are really no established norms to follow. It takes centuries for terms like this to populate the language and its culture.
Really, you have two options -- or more correctly, a mix of the two:
- explain the nature of the relation (once) to anyone who's that interested in it
- make up a relation(al term) that will pass under people's radar, and stick to it.
Counterpartner is a reasonable and logical relational term, which unfortunately means that nobody's ever heard of it, and likely won't understand it.
But maybe it'll make them ask, if that's what you want.
Solution 2:
If you don't want to be friendly, then my daughter’s stepfather might fit the bill [substitute appropriate offspring as necessary]. Why mention the ex-wife/partner at all?