L.R.
Do you mean a short trip (two hours or so) or a long, overnight trip? I think you need to consider the destination -- train travel is great but doing it solely for the train trip might not work; you need to have a destination in mind where the kids will have fun or see relatives or whatever. We use it, we love trains, but with small kids you need to know....
If overnight: you would need for sure to get a "sleeper compartment." This could be a big adventure for the kids, though if they are kids who have a terrible time falling asleep anywhere other than their own beds, or if noise bothers them, you don't want to do this. If they're pretty tough travellers and don't mind the constant loud "chuk-chuk" of the train over the tracks, get a sleeping compartment with two bunks; you and the little one take the lower and the six year old takes the upper. You can sit in this compartment during the day then pull down the beds at night. If you do not get a sleeper, you and the kids will have to sleep all night sitting up in the coach seats; they do not recline, and anyone and everyone can have conversations etc. around you. Sleeper compartments can be expensive depending on the route.
If it's a short "day trip," then coach seats are just fine. On some routes you must have a specific, reserved seat; on other routes you don't have reserved seats and must take whatever seats are available when you get on board -- which could well mean that you and the kids won't get three seats together, which I'm sure you'd want. Amtrak can tell you what the deal is on reserved or non-reserved seats on the route you want.
I have to be honest and say that the bathrooms on Amtrak can be fine at the start of a trip but a real mess soon after that.If your kids are fussy about bathrooms you could have an issue. Some trips, it's messy, others it's not. I would not let that stop you! But I thought you should know.
The food cars are either a "cafe car" with snacks (not good, very limited, runs out of things) or on some trains, a restaurant car with full meals, but the meals dont' offer much choice and I'd imagine there's little for kids specifically. I would not depend on their food service at all and would plan to picnic, though the kids would like a walk to the cafe car for a small snack, just for a change.
Bring LOTS FOR THEM TO DO besides look out the windows. Of course that's the point, the scenery, and they will like that, but at their ages it will not hold them for very long! I took a four-hour ride some years ago where a mom with two kids had brought absolutely nothing for them to occupy themselves and it was a nightmare for her and the other passengers -- she never produced so much as one toy or a deck or cards.
We take Amtrak to get from D.C. to N.Y. which is about three hours plus and it's terrific fun, but my daughter's done it at older ages -- seven, nine, 10. And we have stayed at the destination a few days before taking the train back home. DO take you kids by train; it's a great way to travel. Just think through the timing, destination and routes first. Amtrak will be able to help you --they have always had great phone service! Talk to a real person, not the automated reservations voice. Have fun.