My most recent (thirteenth) ride was this past January; hopefully I can help.A Family room should be adequate to hold your entire party; there are four beds, but I'm willing you could make do with one kid on the floor. or the two smaller ones doubled in one bunk.
As far as fun, Auto Train is Amtrak's best foot forward as a long distance train, as far as kid-friendly, I must say not necessarily so in Sleeper, or at least in the winter season. This is because Sleepers "in season" are catering to the "Bennie Caddie Lex" crowd, and most are not all that tolerant of small children. I have observed passengers with small children taking meals in their rooms.
During the summer season, it could well be a different story.
Coach is probably more "kid tolerant" at any time of the year, but I'm not about to recommend overnight coach travel under any conditions. If Sleeper is not in the economic cards, then just stay on I-95 until "South of the Border"; proceed onward next AM.
Disclaimer: I am not married and have never had children.
[This message has been edited by Gilbert B Norman (edited 03-14-2004).]