We travel the train often, and let me tell you, if you can afford the roomette, it is TOTALLY WORTH IT when you have small children with you.
Another poster is half correct; IF the train is not fully booked, there should be an extra seat for your baby in coach. BUT, if the train is fully booked, you will be expected to hold them. You can call Amtrak to confirm this.
The benefits of the roomette are many. You get a private space with a small table in it. You have a door that can slide closed (which is great if baby is fussy/loud, or if other passengers are loud!). You have a place to keep the diaper bag and gear when you are walking about the train. First class roomettes have a bathroom that is not open to coach class (it's usually much cleaner). We love that table: my husband loves to play cards or put his laptop on it - the roomettes also have plugs, while most of the regular cars don't. On long trips, it's also great for portable DVD players (keeps the kids busy). The table is great for snacks and games for the kids, too. And for us, one of the nicest things is that in a roomette, the bed is COMPLETELY FLAT - you can lie down with your child - unlike the regular seats that only recline (= actual rest). Plus, you have privacy with the sleeper, and your meals are included, and you get to sit in the deluxe lounge (and board first) in Chicago.
There are things you can do to make your trip easier on yourselves. If it's super late/super early/baby is super fussy, you can pay the Red Cap to drive you from the check in counter to the train, and vice versa (I think we tip about $2 per bag/stroller). Depending on which track your train is on, it can be a LONG haul with a small child, strollers, and luggage. The nice thing is that they will take you right to baggage claim, and will usually wait for you! :-)
Buy a carseat bag for your carseat - they have a zippered pouch, and some even have wheels. It'll keep the carseat clean, and it's great to be able to drag it along. You can check your regular luggage, and can even check the car seat (I always put a sign on mine that says FRAGILE, INFANT CAR SEAT), and by law they are not allowed to charge you any extra for checking a baby car seat. They do have an area for carry-on bags & strollers on the train (right when you get on, you can ask the conductor). It's usually on the first floor if you are on a double-decker train.
Don't get me wrong, coach is do-able with a child, people do it all of the time. We've found it's just ten times easier with your own room when the trip is long, and overnight.
Good luck!
M.