You didn't mention which trains you are taking so your schedule is somewhat of a mystery.
Anyway, sleepers are sold on board the train at a substantial discount. However, I have heard that the Florida trains are running packed right now -- especially northbound -- so don't get your hopes up that a room will be available. If you do manage to get a room you should still expect to part with some significant moolah for the upgrade.
Most Amtrak promotions have advance-reservation requirements. Changing your travel dates must be done in compliance with those restrictions (as well as all the others) in order to preserve your promotional discount. Even so, you may not be able to obtain space on your new travel date at the same fare as originally purchased. Plus there is a compulsory $30 ticket exchange fee on most long-distance train fares.
Most hotels in Washington, DC are pretty pricey. If it's convenient, you may want to consider staying in Virginia instead (Alexandria, Pentagon City, Crystal City, etc.) Stay away from the cheap places on the New York Avenue strip in NE Washington -- it's a bad area. Perhaps you could browse the on-line discount sites like hotels.com or even consider booking a package deal through Amtrak Vacations. They offer respectable discounts off hotels when booked as part of your amtrak itinerary.
there are several rental agencies located right in Washington Union station. Unless your planning to travel away from the city any real distance, you may want to save your money and use public transit. DC's Metro system is expansive, safe, clean and inexpensive. A $5 all-day pass is available for unlimited travel during non-rush hour periods. MetroRail (the subway) is supplemented by a substantial MetroBus feeder network as well. Transfers are available in the MetroRail stations.
In general, don't plan too tight of an itinerary where train arrival and departure is concerned. Delays are a common occurance with Amtrak trains, especially those operated over the CSX railroad. Make sure you have sufficient cash with you for food and beverage purchases, or bring your own. While the diners will accept credit cards the lounge cars don't -- and personal checks aren't accepted for anything other than transportation costs.
While the coach attendant will supply those little airline-style pillows to coach passengers you may want to bring your own for added comfort. don't expect to spread out across two seats -- you likley will have a seatmate sitting next to you. Smoking is only permitted in the lounge car, and sometimes only at designated times. If you step off the train before getting to your final destination don't stray far from the door -- the trains usually don't dwell very long at the stations.
