We went to Universal in January with our 3 kids 9, 13 & 16. I would definately recommend buying the ticket that allows you to go to the front of the line. I am not sure what it is called but it is definately worth the extra money!!! (I think it was $20 a ticket) We went over the Martin Luther King holiday which is probably less busy than June will be. We would have left if it weren't for this pass-every ride was at least 45 minutes long! It entitled us to go to the front of the line once for each attraction. It was wonderful!!! We went to the Shrek ride and there were about 400 people in line- we just went to the head of the line, showed our pass and walked right in! Amazing!
We were actually able to do all the attractions at both Islands of Adventure and Universal Studios in one day. You didn't mention where you were staying but if you stay at a Universal Hotel then you get a free pass to the front of the line just for staying on their property. I do think that it will be very hard to take in both parks in one day without paying for the extra pass.
As far as Disney, My oldest son (16) hates roller coasters and spinning rides so he liked animal kingdoms slow paced way. We only went on the Safari and did the walking trail-both were fabulous. On the other hand, my 13 yr old son hated it!!! I don't think you will need a full day there. Keep in mind that AK is the hottest park weather wise to be in the summer! It is huge (sooooo much walking!) and it just seems to hold the heat. Most attractions are outside so plan on being HOT!!
Also, I noticed that you haven't planned any time at the Magic Kingdom! I was afraid that it was going to be too babyish for my kids but we ended up spending 12 hours there! There is space mountain, big thunder mountain, splash mountain, haunted mansion, mickeys philharmagic (in my opinion, the absolute best show) and lots of others that are for all ages not just little kids. Plus, magic kingdom has a great fireworks show called Wishes. They also have wonderful shows and parades that are for all ages. For me it wouldn't be Disney without the Magic Kingdom.
You might want to consider doing something like this

arrange your schedule so that you maximize your time-use extra magic hours if you are staying on property)
full day at epcot definately stay for Illuminations-breathtaking!
1/2 day at AK - other 1/2 day at MGM- maybe take in fantasmic which is fabulous (both parks don't require full days to view everything)
full day at magic kingdom definately try to take in the shows, wishes fireworks and spectro parade-they are all excellent
Of course this is just a suggestion, you know your family's taste. I would sit down and determine park by park what rides you think the kids would like and then determine where to spend the most time. Good luck and have a great time! Any other questions, just ask--Patty