The Superliner Family bedroom is designed to accomodate two adults and two children. You could squeeze three kids in, but it would be cramped. Standard and deluxe bedrooms hold two passengers each, but the deluxe bedrooms include a chair in addition to the two bunks. Two deluxe rooms can be combined into one suite - this is likely what the Amtrak sales rep was suggesting (and quite expensive).
You will be assigned a specific car to sit in, but individual seats are not assigned (your choice). You can request a lower-level seat (the passenger cars on Auto-Train are double-deck Superliner equipment) near the restrooms if necessary; these seats are ordinarily reserved for mobility impaired guests, but are open to everyone.
The smoking room is in the lounge car, but it's supposed to be enclosed and sealed off from the rest of the car (njDISNEYnut's car might have been an older lounge). Feel free to get up and stroll around the train whenever you like - to the lounge, dining car, or just to take a walk (and meet other passengers). I understand that Amtrak tries to group families with children together (same coach), so there may be other children to play with.
Have a great trip!