Bring the police report and so forth. The conductors rarely ask for ID. If they do ask, they'll be perfectly satisfied with the police report, they're reasonable and nice people.
Baggage rules:
https://www.amtrak.com/carry-on-baggage
"Each passenger may bring two personal items, 25 lbs. (12 kg) and 14 x 11 x 7 inches each, and two carry-on items, 50 lbs. (23 kg) and 28 x 22 x 14 inches each, onboard. Make sure you have a tag with your name and address on the outside of all your bags."
("Personal items" means purse, laptop bag, etc.)
"Passengers traveling with infants under the age of two may bring an additional infant item onboard (strollers, diaper bags), which does not count towards the carry-on baggage or personal item limit."
In addition, you can typically bring a pillow and a blanket (intended to be used on the train) . Amtrak is very reasonable about this.
However, you DO have to be able to carry *everything* yourself. Unless you're disabled, they don't have to assist you with your luggage.