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"amtrak is a great idea, but is difficult for us (a mother/daughter) to carry the luggage. but I will keep it in mind in case I can't find a better schedule.... airline reward ticket is "free"..."
Amtrak offers several trains a day with baggage cars, so you could just check your luggage -- free of charge -- at Richmond, and pick it up upon arrival at Newark Penn Station or New York Penn Station. (Amtrak does not offer checked-baggage service at EWR Rail Station.) Even if you were to travel on one of the Amtrak trains without a baggage car, you could check your baggage in at Richmond the day before your trip, and it would be transported on one of the long-distance trains with a baggage car.
Do you have elite status with AA, BA, or any other oneworld carrier? Or do you hold an AA credit card that offers a free checked bag on domestic AA flights? If not, you will have to pay to check bags on your flights. How many bags do you need to check?