If you are staying with enough time to make multiple visits, which parks for you/your family are a must do multiple times park?
First, I would like to bless you for your fortitude and courage going with all of those little ones, those children are lucky to have you
Second, the must see twices for that age group have to be Magic Kingdom and Animal Kingdom. Animal Kingdom closes about 5PM, no late nights and the kids (my 2 dds

ages 8 and 6) love AK and of course MK. Epcot, frankly, is still a bit of a snooze for littles, as is most of MGM barring your Beauty and the Beast, Little Mermaid, Muppets and Honey I shrunk the kids play yard. Forget Aerosmith, Towers of Terror, the Great Movie Ride has the Alien from Alien make an appearance and is very dark and loud. Star Tours is out, The tram ride is okay, but probably won't hold alot of attention other than a possible freak out during the water cascade in the mountains. OHHHHHHHHHH, and please, PLEASE, forget It's Tough to Be aBug in AK - the 3d effect is great and you will loose them (99.9999% chance of this) in the first 5 minutes when the tarantula shoots his butt quills at you - it is intense and there is no way to prepare them for the realness of it. Seriously, after they fall to the floor screaming, they will be hoofin' it to the door and you will be simultaneously laughing, crying, and adding up the pschiatrist bills in your head as you chase after them, they WILL race out of there like a small herd of greased pigs. (been there, done that

, remember,

and

=

)
They will probably love the Magic Carpets of Alladin, Jungle Cruise, Dumbo, Carousel, etc. And they will love the dino dig playground in AK. My kids loved the zoo trail aspects of the park and still talk about the parade. Which feels like you are soooooo much closer to the action than the parade in the other parks, very...involved somehow.
Hope this helps, good luck, have lots of fun. PM me if you have any questions I can help with.