I agree with creditman .... if you can "scope" out empty seats, it will make the ride more comfortable for everyone.
If you have a van you need to arrive at 2:00 p.m. however we were one caught in a major accident and didn't arrive until 2:50 p.m., needless to say we were not the only ones arriving late.
Once you check in with your car/van, you then proceed into the Amtrak building, there you will need to show your i.d. and choose your dining preference time. The earlier you arrive, the better the chance of getting the dinner time you want. We have ridden when there are 2 dinings and 3 dinings, it depends on the number of travelers.
Boarding begins approx. 3:00 p.m. with everyone having to be on board by 3:30 p.m. Although the departing time is 4:00, they begin moving the train to hook up the vehicle cars 15 minutes prior to.
Coach seats are assigned, so there is no mad rush. Once you board, you can see if there are seats available near you. When the train begins to "move" to hook up the car carriers, you will know at that time that no more people will be boarding and you can spread out.
Although you can arrive as early as 11:30, there is no benefit to doing so with children, as there is nothing for them to do once you arrive. I could recommend checking in and then traveling to the a nearby Burger King for lunch. They will allow you to take your car with you after checking in if there is sufficient time for you to return.
Any further questions, don't hesitate to ask.