I think I can give you quite a bit of advice, as I have taken the same route 2 times--from Trenton on the Silver Star on the 8pm train.
The train going there I believe is nicer than the train coming back. We went in June and the dining car was brand new and clean, which was very nice. I would recommend finding the dining car and eating all your meals in it. It breaks up the ride quite a bit and makes the time pass--gives you something to look forward to when the kids are getting restless. It helps pass the time to go have a real, sit-down meal. The food is really pretty decent. The service in dining is very average, but pay the extra money for it to help make the time pass. I found this to be the most enjoyable part of the trip.
If you are in coach, try to get seats located far away from the doors and definitely away from the lounge car, as the opening and closing of the doors can keep kids up at night (adults, too.) The lounge car can get rowdy 11pm-3am, so try to request a seat AWAY from that area, where the drinkers congregate in the middle of the night.
Sharing a toilet with hundreds of other people is fine at the beginning of the trip when the room has been cleaned, but after 20 or so hours with no cleaning and hundreds of visits, it doesn't smell pretty in there. Bring extra toilet paper and some wipies to clean the seat with--this will greatly increase your comfort. If you are sensitive to smells, bring a small atomizer or something to clean the air--seriously these little things make a big difference when traveling in coach.
The seats recline less than 45 degrees, so if you can't usually sleep sitting up, you will only get a few hours at the most. Be prepared for this and just remember you are on vacation and when you get there you can get ALL the rest you need and catch up. We didn't rest well, but some people can. My son couldn't sleep on one seat and needed to lie down, so I let him have my seat so he could lie down across two seats. I paced for most of the night and then ended up sleeping on the floor because he was such a bed hog. Honestly, I really knew he HAD to sleep or it would be a heck of a time, so I sacrificed this for him.
The DVD player is a good idea or if you have a computer that you can play games on, Gameboys, cards, music, snacks, mini board games--anything that can keep you occupied for many hours. The kids will probably have a great time! I think they love train travel. It can be a great way to spend a lot of quality time together.
Just make sure you get plenty of rest the night before you leave and take a shower immediately before you go so it doesn't bother you too much that you don't have the opportunity to shower when you wake up in the morning.
Amtrak is a great deal in coach--very reasonably priced. However, if you can afford the sleeper car, by all means do it. I found the extra expense to be greatly worth it--plus your meals are included in the ticket price if you get a sleeper car--not that that makes it a bargain, but you do get privacy and a bed.
Good luck and enjoy your trip! it is priceless to be able to spend this much time with loved ones.