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Join Date: May 2007
Location: Highland Park, NJ, USA
Posts: 3,798
Bikes: "Hildy", a Novara Randonee touring bike; a 16-speed Bike Friday Tikit; and a Specialized Stumpjumper frame-based built-up MTB, now serving as the kid-carrier, grocery-getter.
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A compromise may be in order here. Perhaps you could do a solo unsupported tour, but let them put you up in a hotel from time to time. Make it clear that you'll stay in touch - cell phone/internet/etc. As Losligato pointed out, difficulty letting a child become independent is gonna be an inherently hard part of parenting.