If you're relaxed, not in a hurry, have an open mind, and are prepared, then you should have little problems.
My three sons and I took the Silver Meteor to Orlando from Wilmington, DE in April 2011.
I researched and took notes, but also decided to just go with the flow, because late trains, crowds, and grouchy people are a fact of life. I saw traveling with Amtrak as part of the vacation experience, so tried to relax and be prepared for any problem (that I could take care of), including sick kids, lol.
It took about 19 hours, and the longest wait was in Washington, DC. We stopped MANY times on the way down/back, (and they allowed people to get off the train 2-3 times, for up to ten minutes) but we took it in stride; if we drove, we'd be stopping often anyway, to stretch our legs, get food, potty breaks, etc.
There's more leg room than on an airplane, and there are TWO restrooms in each car. We did not choose to purchase a bedroom in a sleeper car (maybe next time!), so we made do with stretching out (sometimes sideways) in the seats we were in. You can recline them a bit and there are foot rests, so for a shorter gal like me, it was great. The attendants do give you pillows, but the kids brought small ones, and we all had little flannel blankets to cover ourselves with. I admit: It wasn't very comfortable, but it was a fun experience, and my two youngest sons (7 and 10) loved it. I would definitely take the train again.
We did pick up breakfast AND lunch sandwiches from the cafe car (our ride down was from 5 p.m. on a Sunday to approx. Noon on Monday). They do take credit cards, but it's just easier on everyone if you have some small bills on hand. For the most part, the four of us ate from a small cooler packed with little juice boxes, and tiny, frozen water bottles (which served to keep things cool until they defrosted and we could then drink them). We also brought along dry cereal, bologna sandwiches, granola bars, and trail mix. Next time, I'll pack hoagies.
We were able to draw, color, and read, but also watch movies, play hand held video games, and charge phones, thanks to outlets at each set of seats. We sat across from each other, which was convenient.
The only downside I found to the trip were the bathrooms. Each restroom did get a little gross after 10 hours. I brought a package of anti-bac wipes to help fight that problem, but there wasn't much to be done about the smell.
After departing the train:
At the Orlando station, there is a car rental kiosk, many taxis waiting on the curb, and shuttle vans (backed by Amtrak) to take passengers to their hotels--for $10 a person. I paid the $40 and the shuttle driver took us there (after two other stops). I did not use the service on the return trip (he gave me a card and asked I call at least one day before to reserve a day/time for pick up), because a relative took us to the station.
Over all, I enjoyed it and found it to be much less of a hassle that going to an airport. I'd like to take the train again, not just to Florida, but anywhere!