Ugh! 24 hours is a long long drive!! I hope you get to stay somewhere over night?
One thing I wanted to mention: I don't think arriving that early is so great. I totally get the excitement of wanting to be on the ship as early as possible. But even though they take people earlier, they won't start boarding until some time later (I think it used to be 11:30am?) and the terminal gets horribly crowded. Once people start boarding, the cruise terminal becomes far more manageable. We usually aim to arrive about 45 minutes after boarding starts and by then the terminal has emptied out and it is a really nice and not stressful experience to get on board. We have even started to wait until after 1:30pm before we go to the buffet for lunch. Rooms become available then and a lot of people hog tables until they can move to their rooms. We try to have as little luggage on us when boarding and just tour the ship, maybe get a snack or a drink and then drop of our stuff in our room at 1:30pm and head to lunch. Ever since we started that routine we find that we get into the cruise so much more relaxed! I do understand that the excitement of something new is a very big draw, but especially with kids and after a 24 hour drive, less stress might be something to think about as well. Especially if you are stopping for the night somewhere, you could stop a bit earlier and plan to do the last two hours of driving or so on the morning of and that way you can break up that long drive a bit more?