Are your kids more interested in art/movies, nature/animals, technology, or foreign stuff?
Not doing thrill rides, how long you spend at a park will depend mainly on how much time you spend on things that you'll want to repeat or spend a lot of time doing. Those would most likely be:
AK: Spending time at the Conservation Station/vet area, spending time on the two animal observation walking stations. If your kids are the type who can spend hours petting animals or starting at tigers and elephants, make this a 2 day park.
DHS: Doing the animation academy, watching the stunt shows, taking part in Jedi Training, doing the backlot tour--if your kids really like to draw, or are fascinated by stunts or movies, make this a 2 day park.
Epcot: Doing the interactive games in the Mission: Space and Spaceship Earth postshows and Innoventions, watching the sea life in the Nemo postshow, doing the Kidcot stations at World Showcase countries, doing the new Agent P secret missions. If your kids like technology and games, foreign languages, or Phineas & Ferb, make this a 3 day park (it should automatically be a 2 day park--Epcot is huge!)
If none of those applies, but your kids like swimming and waterparks, consider making both DHS and AK 1 day parks and spending a day at one of the waterparks--you are there in June, after all!
When I was 6 years old, given my love of tech and games, and how cool I would have thought the Agent P missions were, I'd have probably done 1.5 days MK, 3 days Epcot, 1.5 days DHS, 1 day AK.