It sounds like you will be down there in March which means spring break in various parts of the country which means long lines. You could easily spend a full day at either of the Universal parks and see most things but during spring break it will be a challenge. We've gone there for 2-3 days the last couple of years with our kids (now 13, 15). Because of the time of year, we chose to stay in one of the Universal hotels to get the 'express pass' with front of the line access to most rides. It was well worth it even though it was a good bit more than we'd normally pay for a hotel room (ie $300-$400 per night instead of $150) as it allowed us to do all the rides we wanted and included early entry to Harry Potter world. If you cannot change your off-site hotel, you should plan for just 1 of the parks. Look at the rides at each and decide which makes more sense for your family. You can optionally purchase an express pass which will add at least $100 to the ticket cost.

For you, definitely Islands of Adventure. But you can't really do both parks in a day. There are too many lines. If you spend a night in one of the Universal resorts, you can get express passes, and I think that's wroth it.

It depends on what you like. If you want to see Harry Potter then you have to visit IOA. If you are more interested in movie attractions then visit the Studio. If you must visit both parks then you would need to purchase express passes to both parks which could get expensive or as Doug says get a room for one night then you would get 2 days of unlimited express passes (Harry Potter doesn't take express pass).

While Harry Potter doesn't take Express Pass, hotel guests can get in early, though off the top of my head I'm not certain if there are specific days or the conditions. The OP should research that before making a hotel reservation to see if it's a viable alternative.