We have made the drive from Philadelphia suburbs to Disney 6 times with our 5 kids (not all kids on all trips, but 2 trips included all 5). Fortunately, our kids travel very well so we didn't have any real problems with fighting but I tried to make sure they always had enough things to keep them busy in the car so they didn't get bored and resort to fighting for entertainment. They're all adults/teens now so they take care of packing things to do in the car but when they were young, I always made sure to fill a bag with things to keep them occupied on the drive. I always bought a few new movies for them to watch on the drive (they had portable DVD players prior to the days of having movies downloaded on their phones/tablets). I would also buy a new game or two for whatever hand-held gaming system they had at the time (usually just some cheap games). Their bag of "stuff" included paper, colored pencils, stickers, puzzle books, pipe cleaners/Bendaroos etc. -- anything that would hold their interest at that time/age. I also kept a bag of "secret" things at my feet so I could hand out something new every once in awhile -- handheld puzzles like a Rubik's cube were great for killing time. I bought most of the things at the Dollar Store. We also always play the license plate game. Momsminvan.com has a lot of good ideas for keeping kids occupied in the car. Each kid also had their own snack bag that they packed the night before the trip. I would purchase numerous "mom approved" snacks and they could pick what they wanted for their bags. I keep a small cooler of drinks right next to me and hand those out cautiously.

We try to stop every 2-3 hours to get out and stretch our legs -- unless the kids were sleeping, then we kept driving until they woke up. When the kids were young, I took a frisbee, bubbles, and a jump rope for them to use at the rest stop to run off some energy. I always packed wayyyyyy too much stuff (but I wanted to be prepared!) and the kids ended up sleeping for a good part of our drive. We'd tell them they could stay up as late as they wanted to the night before we left.
We always break the drive up over 2 (and occasionally 3) days. We find that once we get past Richmond, it's clear sailing for the rest of the trip with the exception of driving through/around Jacksonville (we usually get to Jacksonville before 10:00 on a Sunday, so there's not really any traffic) and then there's usually some traffic once we get to the Orlando area. We leave home around 5:00 a.m. (which gets us through DC by 9:00 a.m.) on a Saturday and drive about 13-14 hours the first day (including rest stops and lunch). This allows us to be finished driving for the day about 7:00 p.m. We have a few hours to hang out at a hotel pool, have dinner, and still get to bed at a decent time (usually by 10:00). We get up and on the road by about 8:00 and we have about 4 hours of driving left. We get to Disney around noon, have lunch at the resort, do a little unpacking, head to Epcot for FP's & Dinner and then get back to the resort by about 8:00 so we can get to bed early. We hit the ground running in the morning. Now, that being said, based on where you're traveling from, I'd be tempted to do the drive in one day. However, I would not plan on doing rope drop the next day. I'd make that a sleep-in day -- maybe plan a special lunch followed by some time in a park. We split the drive over 2 days so we aren't exhausted when we arrive. The last thing we want to do is feel like we're sleep deprived when we're starting our vacation. We are fortunate because DH has 28 days of vacation to take and I don't have any vacation time constraints so we can "afford" to add extra days to our vacation for driving. I know not everyone has that luxury.
We choose not to drive during the night for a few reasons. The first one is that because our kids travel well *and* they sleep for a good part of the drive even during the day), we never felt the need to. But we were concerned that neither one of us is used to being up during the night so we don't feel we would be alert enough to drive safely through the night (or we would have to adjust our sleep schedules for 2 or 3 days before leaving and then again after arriving). Also, we couldn't ever quite figure out the logistics for driving all night...if the parents are awake all night (one parent driving, the other serving as co-pilot making sure the driver doesn't get too tired or fall asleep) and the kids sleep all night, what happens in the morning when the parents are ready to sleep and the kids are raring to go???? Leaving early in the morning worked fine for us -- the kids usually sleep for at least the first 3-4 hours of the drive. I know plenty of people do the "drive all night so the kids can sleep" thing, but it just never made sense for our family.