He was appalling, but frankly you both need to give your heads a shake and need to act as parents.
All of you (or any of you) going home, with all the costs of that, is frankly ridiculous. If you are going to separate (which you should), you'll need to be able to communicate enough to coparent. So for goodness sake grow up the pair of you, and start co-parenting and learn to be civil now.
If you go home, check in as a family, sort out the luggage and kids and faff as a family.
Though why you'd want to throw away thousands of pounds on an all inclusive holiday to come home on day 2 rather than try and make the best of it, I don't get.
If he wants to go home, can someone come out to you to replace him and help? It would be cheaper than all the new flights.
The poor kids don't deserve to be stuck in this. The fact that (1) things escalated so quickly and to you throwing things - albeit only a hat, and him storming off and disappearing and (2) you were so chilled about him disappearing that weren't going to worry until tomorrow, makes me think you have a volatile relationship normally.
It's clear you guys need to split - this is a horrifically toxic environment for everyone, especially your kids, but you do need to both act like grown ups now and not make any rash decisions.