Hi, we've been on two previous Disney cruises, but several out of Pt. Canaveral with two small children. We always drive from Georgia the night before and stay in a hotel in the area. We've always gotten to the terminal (or whatever you call it) early in the day, check in with no lines and then sign the kids up for the kid's programs with no lines also. It is a good thing to sign the kids up here, because the lines get so long once registration begins on the ship (at least they were our two times).
Both times, i want to say we boarded around noon since we were in the front of the line. This isn't the official boarding time, but i think as soon as the ship is ready to take guests, they begin the process. They have you go straight in and up to lunch first. The first Disney one we did was when my daughter had just turned 4 and my son 6. I do suggest to get there early, just becuase the terminal gets really busy. They have Disney shows playing on tvs, coloring for the kids and a couple of the characters walking around to pass time for them, but for the costs of the cruises, we like to have that first day be an actual vacation day. After lunch the kids go swimming before the ship sails (and I'm assuming you've read about how cool the kid's pool is. I've never been to a pool with my kids before and just let them go by themselves without worries until we went on this cruise!) Anyway, the pool isn't as crowded if you hit it on the earlier end, but later in the afternoon it's pretty bombed since every little kid sees it and HAS to go in!!!
We've stay two times at Radisson at the Port which offers free shuttle service to and from the port as well as free parking while on your cruise. It is ok and has a really nice pool. We've also stayed in smaller, cheaper little places, but my husband hasn't liked any of those! I can feel good recommending the Radisson. I do know that I'd book the reservation early though, because, both times we had checked prices early on and then when we actually booked, the prices had gone up. We always book through Expedia, Travelocity or Orbitz.
Just a thought, if you end up flying in the day of the cruise, have you checked into Disney's bus transfers instead of a rental car? We've never personally used them since we always drive from Atlanta, but i know people who've had good experiences. Keep in mind that parking at the port costs I believe around $12 a day, so depending on your length of cruise, this could add up.
Hope this helps! We're taking the Disney Magic with the kids this June out of Barcelona, Spain for their 10-day Mediterranean cruise and can't wait!