Here's another story:
I'm also still not clear about whether a) the toddler was the cause of the 15-minute delay or b) there was some other kind of a delay so they were in a hurry and not in the mood to give a second chance.
It does sound from phrasing like there wasn't a warning or a reasonable chance given for the parents to snap to it, just "that's it, you're out of here."
The hitting thing from Linkat's longer account is patently stupid, that they kicked them out because the toddler hit the mom (that's what the "doesn't matter if she's 3 or 33" quote came from).
If the toddler was the cause of the delay, or a few more if's, I think the airline is justified.