If you get on after Penn Station, you should have no problem finding seats together. By Philadelphia, you are in trouble though. We have taken train 97 down twice, and both times (once in June and once at the end of September) the train was full. However, we didn't have any trouble finding seats together, as we got on before Philadelphia.
Some tips...
With kids...get a seat in a car as far away from the lounge/eatery as possible...the farther away you are, the less traffic--especially at night when the kids are trying to sleep. The lounge car can get downright rowdy from about 10 p.m.-2.a.m. If you are far away from the center of it all, there will be less traffic and less door opening of people going back and forth.
Also, if you are sitting in coach, plan to eat in the main dining car a couple of times. It really breaks up the trip and makes it much more enjoyable. The prices are pretty reasonable, and the food is pretty good, although typical fare.
Additionally, I would take ear plugs, Benadryl for sleep for you (and the kids probably, too,) and a favorite blanket and/or pillow, plus lots of snacks, games, and if you have one, a portable DVD player. We also brought a mini-TV, although station reception was spotty.
If you can afford, spring for the sleeper car. It is well worth the money. The first time we went down we went coach but decided on the sleeper for the next time. It was a much better night's sleep.