OK, here's my two cents as a mom of 11 and 8 year-olds going in June

:
1. Stay onsite. Besides great hotels with great pools, you get Express Access (think unlimited fastpasses) for every ride except Rip, Ride Rockit, Pteranodon Flyers, and Harry Potter and the Forbidden Journey. Royal Pacific is the least expensive of the three - we are paying 228 per night for four nights from June 12-16 (rack rate is about $270, but you get a discount if you stay longer). If you have
AAA, there is generally a discount, but you have to call.
2. By staying onsite, you get early entry to the Wizarding World of Harry Potter (you can also get this with some off-site packages). Totally worth it - we went last July and it was so great to get in early. Besides being very hot, that area in particular is very crowded.
3. If you stay onsite for one night, you get Express Access for your check-in and your check-out day. You could do Universal Studios on your check-in day, then Islands of Adventure (since you will want to be there early) on your check-out day.
4. Unlimited Express means that if your child wants to ride Flight of the Hippogriff 17 times in a row, you can get in the express line each time if you stay onsite. We rode Cat in the Hat over and over because it was very hot and the queue for Cat in the Hat was freezing - it was our air-conditioned break with no waiting.
What to see (based on my kids, so your mileage may vary):
At IOA:
8-year old loved Hippogriff (much better than Goofy's Barnstormer), all of Seuss Landing (don't avoid One Fish, Two Fish because it looks like Dumbo if your kids think Dumbo isn't cool - OFTF is awesome!), all the water rides
11-year old loved all but Hulk and Dragon Challenge (didn't do those). She especially likes Spiderman and HP and the Forbidden Journey. She likes One Fish Two Fish and Cat in the Hat, so I do disagree with the PP who said to skip Seuss Landing. I find my kids (even my 11-year old) will ride rides at Disney and Universal that might be designed for younger kids and will love them, since they don't have to worry about looking cool. Seuss Landing is one of the best themed lands in Orlando.
At Universal:
Mummy was closed the day we went, and RRR was broken down most of the day. DD11 liked everything else. DD8 liked Jimmy Neutron, Shrek, Woody Woodpecker, ET, the Curious George water play area, Disaster. She liked Jaws ok but didn't really like MIB - she thought the aliens were creepy, but they are really not scary. My DD8 is not that adventurous when it comes to rides.
For Forbidden Journey, you can't take bags on the ride, so I'd either try to go without bags that day or be prepared to take a few minutes to put it in a locker. If your 8 year old won't ride FJ, you can all walk through the line together with the bags, then do child swap at the end so your 11 year-old can ride twice. There is a separate castle tour line as well, but we stayed together and DD11 rode once with DH and once with me.
If you want to do the show at Ollivander's, do that first. The line gets very long and only about 20 people are let in at one time. Only one person gets picked to have a wand choose them - just FYI in case you need to prepare your kids that one or neither of them might get chosen.
I can't stress enough the importance of staying on-site with kids - the perks are way better than on-site perks at Disney. The heat and crowds can make or break a vacation with kids, and the express access allows you to avoid the longest lines and gives you the flexibility to try a ride that you might not want to wait 30-45 minutes for, but you would be willing to try with a 5-10 minute wait. Even if you stay at the Doubletree (or somewhere else) for most of your stay, I'd try to stay on-site at least for one day.