Gaelicslog - I have been in that exact position, also with "well-known Irish budget airline".
Back in the days when seating was first-come-first-served, we were caught in traffic and almost missed the plane. So when DH, myself and DS (5), DD1 (3) and DD2 (1) got on board, there were precisely four seats left, dotted all over the plane. DS and DD1 sat together near the back, me on my own in the middle, and DH (with DD2 in a lap belt) at the front.
No member of the cabin crew attempted to seat us together, or showed any concern that we were separated, and no-one offered to move. And I was so embarrassed at being late on board that I didn't ask anyone to! Leaving DH with DD2, I spent most of the flight running up and down the aisle, or sitting on the floor in the aisle next to DS and DD1. Despite being 3 and 5 they were good as gold, although at one point, DD1 needed a wee, and I couldn't get past the drinks trolley, so the lady sitting next to her had to take her. DS also spilled yogurt all down himself. By the time we landed I was a sweating, frazzled wreck. Heaven knows what would have happened if they'd tried to get to me during takeoff or whatever.
So I guess what I'm trying to say is, don't expect the cabin crew to care, don't expect people to move (although strangers can be kinder than you think), your children possibly will survive a flight without sitting next to you and, most of all, if it's important to sit with your children pre-book your seats, and don't be last to check in!