What people are saying is to do it on her terms, as a cold decision - not in the heat of the moment - and that is correct.
I had suspicions earlier, but we were in the middle of buying a house, so I figured why would he do that if he wasn't invested in the relationship. Anyhow, it turns out he was just a lazy idiot who re-wrote history in his head so I would be OK with it. Result being I walked away with a house as well as maintenance (not married, not in the UK, other assets split differently). If I had my time again, I would have taken half the money in his account (that he had me manage for him), but I thought he'd manage to be reasonable and adult about the split rather than immediately running away to another country with a new girlfriend.
TBH OP, keeping it cold is for the best - all the women I know who have blazing rows with their exes, have a much worse time than me who just ignores his existence apart from calendar invites and the occasional email regarding pickups. Not that I'm perfect, there was some tears and yelling that first week - but it didn't get me anywhere, I can see that now.
I doubt he'll bother with them beyond the occasional day trip (that you'll have to pack for), and yes, it's scary, but not as bad as all that, but I can also see the argument for giving it a couple of years if you can, so that you can get yourself on a safer financial footing childcare/job-wise.