How long was the holiday? If it was a weekend then you're right, if it was two weeks then you're not. The holiday has to be for her as well surely?
You seem to think she should do what you "point out", doesn't work like that with women, has the opposite effect in fact usually.
As for her ex sleeping on the sofa, that's great and fine, no problem there and she hasn't done a damned thing wrong on that count.
The holiday I'm ambiguous about, it depends on timescales, but sit down and talk to hr about it without rowing and see what her point of view is.