A private van is not a bad idea at all. Miami rush hour traffic can be intimidating to the uninitiated. It's not horrific once you get north of the spaghetti bowl, but having someone else do it is the way to go. Especially dealing with a party your size that just sat in a flying can for 13 hours.
Leaving Orlando on a Sunday there is going to be some traffic, but honestly it won't be as bad as the morning rush hour coming north from Miami, at least in my experience.
Just figured I'd share some local knowledge for you. I've made that drive from Miami to Orlando and back at least 100 times both for work and for vacation.
"flying can"......great description!!
i did that drive exactly once....orlando to ft lauderdale...
it was on a sunday morning...
just four of us (DH, me, DD and DSIL)..
i had it all planned out where i would stop on the turnpike (halfway there, don't recall which stop)..
but i was soooooooooooo tired i ended up stopping at every single station on the turnpike..
we parked, walked into the bathroom, i bought a cup of coffee from whichever fast food place was there, and then we were on our way..
i was completely falling asleep the entire way, but thank god i made it to port everglades (for our allure of the seas cruise)...
it was the latest i've ever arrived for a cruise....i think our port arrival time was 10:30, but we ended up getting there at 12:30 ...
on the bright side, when we boarded, the staterooms were already open so we could drop off our bags right away...silver lining!!!
so yeah, attempting that drive after flying for 13 hours and being up for who knows how many hours before that organizing, definitely a recipe for disaster...