Posted 29 June 2017 - 03:38 PM
Even though there are checked baggage options going to the Grand Canyon (transfer point of Flagstaff instead of Williams Junction, Thruway ticketed bus services to South Rim available at Flagstaff), Waterloo itself does not handle checked baggage, so checking things is not an option.
Informally, the train crews generally allow you to carry on anything you can do in one trip (no going back to the platform for more). So if you can handle the double stroller and your luggage while wrangling the kids, probably no problem with Amtrak. At worst, you'll probably get hit with the relatively new excess carry-on fee of $20/piece. The crew can generally find a place to stick things (these are not airplanes, after all), in coach in single level equipment, at the end of the car, in Superliners, the luggage rack downstairs, although in coach that can get pretty crowded.
You better not expect to carry that thing onboard an airplane, though.
Pre Amtrak: SP Coast Daylight, AT&SF San Diegan, AT&SF Super Chief, D&RGW Rio Grande Zephyr
Amtrak: Southwest Limited/Chief, San Diegan/Pacific Surfliner, San Joaquin, Cascades, California/San Francisco Zephyr, Coast Starlight, Empire Builder, Sunset Limited (LA-Orlando), Desert Wind, Pioneer, City of New Orleans, Silver Star, Silver Meteor, Lake Shore Limited (NY Section), Cardinal, Hoosier State (Amtrak), Hoosier State (Iowa Pacific), Ann Rutledge, Adirondack, Maple Leaf, NE Regional, Capitol Limited
Via Rail Canada: Via Canadian (CP route), Via Super Continental, Via Atlantic Limited, Via Hudson Bay, Via Skeena, Via Canadian (CN route), Via "Corridor" (Toronto-Montreal)
Other: BC Rail Cariboo Dayliner, Alaska Railroad, Eurostar, Thalys, DB, Netherlands Rail, Austrian Railways, BR, Korail (conventional), Korail KTX