John,
In a deluxe room, there is a toilet/shower closet right in your room. I say closet, because it really is tiny. In fact Amtrak actually has a sign in the closet suggesting that you sit on the toilet lid, while trying to take a shower. I'm 5'11" and weigh 160 and I'm smashing my elbows into the walls when I try to shower in the deluxe room's shower.
So I normally go downstairs on the Superliner cars, the double decker cars, and shower in the public shower. That public shower is right down the hall from the family bedroom, which is also on the lower level of the car.
Please note that the single level sleepers, the Viewliners, that you would encounter should you ride east of Chicago, does not have a family room. It only has deluxe and standard rooms.
I would also mention that your kids would need to be approximately 12 or under to use the family room. The kids beds in the family room are only 4' 9" so if your kids are taller than that, you will have to get either two deluxe rooms or two standard rooms.
You can find diagrams with dimensions of Amtrak's bedrooms by clicking
here. A virtual tour is available
here. Next,
this link will show you the basic layout of Amtrak's sleepers so you can get an idea where the rooms are in relation to the shower and public restrooms.
Finally, you might wish to check out
these travel tips from On Track On Line, which is chocked full of hints, tips, and what to expect from an Amtrak train trip.
Hope this helps some. If you have more questions, please don't hesitate to post them.