These caretakers will benefit from being left some prepared notes and/or a simple list of instructions. It is surprising how poorly many people feed small children, and you can head off problems by stating your expectations clearly. Experienced babysitters are used to dealing with family differences and shouldn't be fazed by a list of instructions. Many sitters will usually be grateful for the help.
As you prepare the meal or snack, or a general suggestion list, make sure to include tried and tested items you know your child enjoys, saving less popular items or new foods for Meals when you are home. As a general rule, try to provide a quarter more total food you expect your child will eat and tell your babysitter that your child is unlikely to want it all -- and that that's fine.
Sometimes an otherwise wonderful babysitter will do some things that make you cringe. Maybe she persistently tries to overfeed your nine month old baby when he is clearly full, because she firmly believes she knows best about how much babies need to eat -- or keeps putting your four year old off different vegetables by educating him about how healthy they are. Good child care is hard to find, and you probably won't want to replace your sitter just because she or he is in a different place from you when it comes to eating.
If clear instructions don't help, reduce the amount of food you leave and shift the makeup of individual meals so that the most important foods get eaten only when you are there. In particular, fruits and vegetables are foods you want your child to like, because it is hard to make a healthy diet without them.
Let's say your babysitter gives your child lunch and snacks. Make breakfast and dinner the two meals that count most. Fresh fruit with breakfast every day, fruit and vegetables with dinner at night, and all these items on weekends, too, will go a long way toward preventing your babysitter from creating unnecessary diversions. Lunch and snacks can be familiar items -- either without fruit or vegetables, or perhaps let your babysitter offer just one or two favorite fruits. Alternatives such as soup, sandwiches, and cookies can always be replaced with other foods if dislikes begin to set in.