Perhaps having a room makes all the difference...
We definitely sleep better in a room than in coach ... but mind you, I am 6' tall and my DH is 6'6" tall so those coach seats, albeit very large, are just not made for tall people.
When we arrive in FL and have our vehicle, around 10-11am-ish, we go straight to McD's for some food to eat along the way. Then a quick stop at
Walmart and we are at our hotel by 11:30am - 1pm at the absolute latest.
We go straight to our room and if it's ready, check in. If not, then we go into a park or explore our hotel, esp the pool and playgrounds.
I think our best was in Epcot by 12 noon!!
A night without a shower is no big deal, esp if you took one the day you boarded the train.

Just brush your teeth and take a towel on your face. Use deodorant.
We are well-rested from the train ride down -- no worries about accidents, traffic, are-we-there-yets, unexpected bathroom breaks, where to stop for food, running low on gas, construction, thunderstorms/snow, kids fighting, cramped seats, seat belts restricting our movements, can't get up and stretch, wear and tear on car, other drivers who are driving sleepy or drunk when they should just get a hotel, etc.
We drove to FL twice ... arrived tired, cranky and worn out from it all. It was actually a bit better for the person driving ... the other person who had to help entertain and referee the kids was worse! Maybe if the kids were older and could easily entertain themselves and not get into arguments all the time, it would be different.
On the train, we can separate the girls when they need it. Or I can separate myself when I need it!
Oh, and stopping in some of the worse parts of Jacksonville, b/c our daughter had to pee ... even though we just stopped about 45 minutes earlier?! I thought for sure our SUV wasn't going to be in one piece anymore...
With the AT, we actually slept the night before... had a leisurely night in fact with a sit-down dinner, snacks, movie, wine. We go to sleep earlier than we normally would on the train and everyone gets a chance to sleep -- not just one driver for 4 hours.
Like PP said, it's part of the vacation -- an adventure and fun way to travel.