I know you're saying you'd rather do that THAN use the nasty rental car carseats. I know you wouldn't really do that.
Amtrak's
luggage policies:
3 50lb bags checked EACH. 2 carryon bags EACH.
NOT INCLUDED in these limits are "personal items such as purses, briefcases, laptop computers, baby items such as strollers, diaper bags and
car seats, and equipment required for a passenger's medical condition such as breathing assistance devices and oxygen tanks."
Honestly, you can take on far more than you guys will be able to carry.
The only oddity about Amtrak and carryons is that generally the space AT your seat is relatively small, and you'll be leaving the bulk of the carryons in an unmanned luggage bin (on west coast trains it's downstairs while seats are upstairs). So bring those luggage locks and luggage tags!
Of course you know you won't be able to use the seat while ON the train, but it will be helpful to have it once you're there, even if only for the ride to and from WDW.