2nd vote for UPack! Very professional, smooth-running service when we used it. The only problem is finding a place to park that giant trailer. Also, you might want to have movers to help load it because it's really hard to stack your stuff that high.
FYI Penske is often cheaper than U-Haul for one-way moves.
It IS an option for one of you to drive the truck and one to drive the car. Mr. FP and I did that for 1500 miles.My kids were older than yours--ages 2 and 3 at the time--but obviously there were two of the, they had higher activity needs, and at the time, neither of them was fully potty trained. (We also had a cat with us.) We really wanted to keep control of our stuff and not have to wait for it. I'm not gonna lie, it was excruciating, but it was also temporary. Whole thing was over in a few days.
Our truck broke down and we were stranded in Strip Mall, Ohio, for five hours, but we negotiated an $800 discount off our quote, so that's $40 per person per hour--not bad!