The hotel should be charging by the MEAL, not by the chair. That's ridiculous. A child's meal doesn't cost what an adult meal does. Most places charge a child's fee from 3-10 or 3-12 years old, and free for less than that. They're only going to eat off your plate or eat what you brought from home anyway. The synagogue seder planning committee or the rabbi should intervene on this one.
Also, the synagogue should hire the babysitters, not the hotel. Hotel sitters aren't going to risk annoying the paying parents. Most synagogues have a group of sitters who babysit on Shabbat or at High Holidays, and therefore could sit on Passover - usually there are some who are not Jewish and therefore are not otherwise celebrating. The problem children aren't going to be overseen by their own parents anyway, who should be at the seder.
I think it would make more sense, if your children are too young to participate in a large group seder and if it's not going to be interactive enough to engage them, to leave them at home with a sitter of your choice. I understand that Passover is important, but you are not having an in-home seder where the kids can get up from the table and come back at the important moments.
If you are going to put your children in the babysitting room, then you can and should say to the adult sitters that some kids like to act up when out of their parents' view, and you are concerned about your little ones with larger kids. Don't single out the specific mean children you have in mind. I wouldn't worry so much about what your children will "learn" from these other kids - bad language, bad behavior? At 2 and 1, they are unlikely to pick up too much. And you say yourself that your own children will want to fight with each other. The bigger problem is injury. I think you can suggest that the sitters divide the children by age group, with toddlers in one place and ages 4 and up in another area or room. Makes sense from the standpoint of activities, toys, and so on. And the hotel is absolutely liable for what goes on under their roof if they are supervising the children - while you can't go around saying how much you don't like someone else's parenting style (or lack of it), you can let go of having to manage every second of it.
Either take the kids and enjoy the seder, allowing the professionals to watch the children, or have the kids stay home with your own sitter so at least you can enjoy the seder. You will have plenty of years for your children to enjoy Passover.
And by the way, we always do interactive seders with silly songs and "plague bags" and holiday-related themes. So there are lots of great ideas to keep children engaged either in a kids' seder (which some synagogues do during the day before the actual holiday) or at home. Let me know if you need some time-tested ideas.