I Can only advise on the 15mo as our one is only 18m now. Butwe have done this a fair few times so I have it cracked for us. Sleep is the best option, try to get an afternoon / evening flight. Make sure thy run around a lot at the airport to wear off excess energy before the flight. Eg make then walk to the gate. When you get on the plane or just before give "tea" even if it's 3pm. Start doing queiet activities such as reading. As soon as the seat belt sign goes off get the bassinet for the 15mo. When you can, brush teeth and give milk for bed time then put to "sleep" in the bassinet.
Regarding food you could take pouches and cartons of pre mixed formula for 15mo. Remember to take twice as much as you need. Airport security make you open and taste 50%.
I've travelled quite a bit with my DS- now coming up to 3. - top tips: with the older one, if you have an iPad/iPhone download their favourite series onto it, and then look on amazon for children's headphones. This has been our real godsend. - with the younger one, buy a couple of new toys and do not let him play with them until he's on the plane. Nothing too noisy but the novelty will hopefully pass a few hours. - Richard scarry books have been good, but can't remember what age I started reading them to my son. - carry everything in a rucksack to free up your hands. - remember that you can take your buggy up to the gate, but it will be delivered back onto the carousel- so you will need to carry youngest child. - take a change of clothes for both children just in case. - don't over stress... It won't be as bad as you fear, people are generally sympathetic and children fly all the time- have a great holiday!