Sorry, not buying the "add 33% for food, bathroom, and gas breaks". That basically equates to driving an hour, then stopping for 20 minutes (I think my math is right).
Use google maps to check the miles from home to the resort. Divide the miles by 60. That should give you a pretty good idea of how long the trip will take. Yes, many speed limits are 65 or 70, so you go 7-9mph over. That extra speed makes up for the stops.
Stops are where you REALLY lose time. Ideally, each stop you get gas, go to the bathroom, get some food (to go), and get back on the road.
Yes, I have travelled with toddlers and infants (at the same time).
I would drive it in one day (the day before check in), get a hotel about 30-60 min from Disney, get some rest, check in the next day, and take advantage of the water park.
I agree with
@Lewisc, DON'T make hotel reservations and see how things go. If they're going poorly, the navigator (presumably the OP) gets on their phone and looks for hotels 30-60 minutes away. If they're going good, then you get all the way there.