Svetlana,hello!
If you still did not decide exactly the park in the USA, then for small children is better to start with Disneypark in Paris. So many attractions for little kids! The best age for children for Disneypark in Paris is 5-8 y.o. Children under 5y.o. are still very little for such kind of amusement, children with age 5-8 will find a lot of things to enjoy. Also each quater of park has own theme shop- so prepare ur money for Princess' dresses, shoes, crowns, etc, as well as for boys' heroes. U have wish to buy many beautiful things on every step. Hotels are great- with disney characters (Pooh, Donald Duck, etc.) during breakfast time. They play with children, make photos for free. No need to stay n the main Disney hotel (close to the main entrance to the Disney park), some other nearest hotels are also v good, with shuttles every 20 mins to the park and back (only 5-7 mins to drive). I brought my son to Paris Disney park when he was 9y.o. and he enjoyed fully as was no heigh limitation (usually it's 138-140 cm). Do not try to cheat park staff with children height as later you will regret- it could be dangerous for child,his life & health as all belts consider child or adult higher than 138-140 cm if some particular attraction has such limitation. This summer we go to Orlando bcz son is 11 y.o..We want to try more than in Paris, but to START with Orlando I'd not do. Also some very good parks in Europe are Gardaland in Italy (2-3 hrs by train from Milan), Port Aventura (abt 1hr from Barcelona) and Legoland close to Munich. Great for children under 8 y.o., as well lots of fun for parents.