This is all off the cuff here, but:

How 'bout flying into Pittsburgh, rent your bikes, and drive to Youngstown using a one-way U-Haul rental truck? If you can get a rental with a bench seat, the three of you should be able to fit. The ride to Youngstown isn't that far. I just did a quick check at a U-Haul location here in Pittsburgh for a mid-month rental. A 10' box van would cost $110 for a one-way rental to Youngstown, OH.

You can rent bikes here:

http://www.bikepittsburgh.com/bikes-and-rates

There may be other places to rent bikes here, but I ride past this place frequently, so I know they do. Since they rent for the Great Allegheny Passage, you should be able to get bikes with a rack and panniers.

Hope that helps. I like stories where one generation of people is reconnecting with their past through pursuit of recreating some great adventure. Good luck with ride and please post back with a report how your planning goes and of the ride itself.