I wonder how much luggage they have, if the Caltrain is not an option. It sounds as if it would be a struggle anywhere, LHR, JFK, SFO with a lot of luggage.
Personally, large suitcase per person, not a problem on Caltrain. Has luggage racks too. If its the matter of getting it onto the train, due to steps and not being able to lift it, it could be a thing. I can't quite recall if there were significant steps onto it, I might well be confusing it with the Amtraks about the area, which I've used a lot more.