A cool bag, food from the fridge, and an icepack from the fridge should keep things cool for one meal.
What about a bought pasta salad, fridged and cool baged for first meal (or 2, one for each child!?), I'd think baby bel or other "plastic", pre-wrapped cheese would survive. Yoghurt tubes claim to be OK for 8hrs out of the fridge (liquids through security).
You can buy pints of milk airside in most airports (tho we have had to get semi occasionally). Could you get the mini packs for cereal, and either eat dry, or add milk?
Breadsticks? Cheese straws? Mini chedders?
Can you find any individual pots/tins of fruit which are under 100ml? Or dried fruit.
I'd go and investigate the kids lunch box sections of the supermarket, and think what would be OK for 3 weeks in a suitcase before coming back! Does DD2 get a hand luggage allowance as a lap traveller?
Flying the other way we had free reign on the snacks left out in the "kitchens" - biscuits, crisps, mars bars, those cheesy biscuits. I've also asked if there is any fresh fruit going spare from first class before, and its been produced.
It sounds like a bonkers rule - and I'm sure if the cabin crew want less stressed parents, and less screaming kids, they will let you have an extra meal! They were very helpful when they thought I was lone travelling with 18 month DS2 and 3 yr DS1 (because they had split the 4 of us up on a 13 hr flight......).
Enjoy your holiday - if it comes to it, 12 hrs of junk isn't going to be the end of the world!