It sounds like you have a great trip in the works for this summer! If you are planning on visiting only two parks, I would first suggest the
Magic Kingdom as it epitomizes the Disney experience for me and has a great selection of attractions for all ages.
The second theme park is a little more difficult to decide, & I'd really encourage you to get input from everyone.
Disney's Animal Kingdom has 4 thrill rides and a wide selection of attractions for all ages, including two Broadway-style musicals.
Disney's Hollywood Studios has 2 thrill rides & attractions for all ages. It also has areas devoted to Star Wars and Pixar.
Epcot has 2 thrill rides, many dining choices, nighttime fireworks & lots of chances for exploring.
To help determine the must-see attractions, I really like using the touring plans at www.touringplans.com as it offers plans based on different ages' and groups' interests. It does have a small fee, but one that I think is a good investment for planning.
My family really likes the water parks, especially
Disney's Typhoon Lagoon Water Park because of the wave pool; they could spend hours and hours there. There are also children play areas for your little ones. You may honestly find, however, that you'll be plenty busy with just the theme parks. If your resort has a pool, that may be all the water fun your family needs. Also, June can often be unpredictable with spontaneous rain and storms.
I hope this helps; please let us know if we can help further.