I would do both Disney and Universal and take all kids to both. We went to Universal with 4.5yo and 6.5yo last year and they had a blast. We bought a wand and they loved doing the spells.
Are you going during a school break? Then I agree you should stay on site for early entry and the free express passes. We went to HP for the early hour and then we got to go on all the other rides with less than a 15 min wait. We went to both Universal and Islands of Adventure. Plenty for the little ones. Dr Seuss, Marvel, Minions, ET, Toon area, shows, parades.
If you are going with multiple adults and kids, you could split up and meet back up pretty easily. We needed a mid day break. The parents were just as tired as the kids. We'd go back after lunch, rest, swim and then sometimes go back to the parks.