You're not likely to be separated from your children in the first place; if you are, people will probably be willing to switch with you.
If not, here's how to handle it:
Begin by telling the person seated next to your child --the one who insists he or she cannot move -- that the child has really been a handful that morning, and secretly you're glad for the rest. Begin by explaining that the child is a bit fearful about flying, but if the adult will just talk to him throughout the take-off process, he should get over it without much of a tantrum -- too bad he's too young for gum. He did have that ear infection last week, and the take-off could be painful to his ears. Then open up the child's bag and explain that you've brought along crayons and coloring books, and they should entertain him for 15-20 minutes -- caution the adult that he does like to throw crayons, and do make sure he doesn't put them up his nose. There was that Emergency Room trip, but, oh, why talk about that now? After that, it'll be time to read a couple books -- here they are -- the child does so enjoy when you read with enthusiasm and use different voices for the characters. Oh, and you're really sorry that you forgot to give the child some motion sickness medicine before you left the house, but he's only thrown up twice before in the car, so it should be okay. At this point, you show the child the barf bag and say, "Remember what Mommy said this is for?" Demonstrate just for good measure. Before you have time to bring out the child's snacks, the adult will be begging to trade with you.