I've been the one in charge of splitting the bill for lots of group holidays. Lots of adults, lots of sub-teenage kids.
I count kids as one share, adults as two. Everyone seems happy with this.
In your case, there are 3 adults and 4 kids in your party, so that's 10 shares altogether, of which you pay 4.
So if I was organising the bill split, you'd pay 40%, they'd pay 60%.
Even on a per-head basis (one share each), you should only be paying 3 out of 7 shares, which is about 43%. But that ignores adults eating more than kids and drinking booze too, really you should be paying less than 43%.
At the end of the day, we're talking about 10% of the overall bill so only you know if it's something to be wound up about. But personally if I was on holiday with people who weren't up for a fair bill split, it would make me less eager to go on holiday with them in the future.