Hi,
We made a point of being at the port as soon as possible after 10 am, and as other posters have indicated, there is lots to do at the port. While one parent stands in line, the other can be in the kids club lineup getting the pager and the kids' wristbands. If you do the online checkin, the registration process is pretty painless. We had Boarding Pass 6 and we were on the Magic by shortly after 12 pm. As a result, we ended up having a full afternoon of activities - toured the ship, had a wonderful lunch at Topsiders, swam in the pool, etc. At the end of the night, I felt like we had a full day on board, not just a few hours.
Also, keep in mind that if you don't get your Palo reservations that you want online at 75-days before your cruise departure date as a first-time cruiser, you are going to want to be there ASAP, as the remaining Palo reservations are doled out in Rockin Bar D on a first-come, first-served basis. We ended up on a waiting list for our Thurs brunch reservation, even though we were on board at 12:30 and went straight to Rockin Bar D. So, if you don't yet have your reservations, and that is important to you, it's a good reason to get to the port as soon as possible on Sat. a.m.
As you read through the DIS, you will see that many travelers fly in the night before and either stay at the Hyatt at the airport, or even at a hotel near the port. That might be worth investigating...
In terms of the day of departure, keep in mind that you will all likely be very tired. We had kept our kids up late since the middle of the week due to various activities - pirate night, 11:15 dessert buffet at Lumiere's, final greet session with the characters, etc. and then you have to get up very early on the Saturday. The entire busload of cruisers going back to the airport on the Saturday morning were basically sound asleep. I am not sure that a big day of activities would work out well on the Saturday, even though there is time for it... It would be interesting to see what other DIS'ers say about outings on the Saturday after the cruise. In addition to exhaustion, we were so sad that we were leaving the Magic - I am not sure we would have really enjoyed anything else that day, and it was just as well that we headed straight to the airport and home.