Hi Florence!
All encouragement your way!
I think combining geocaching with family cycling is brilliant. For some years, I placed and maintained a series of 25 geocaches, and many were specifically family/child oriented and those were the logs I enjoyed most. Many parents related the joy of cycling or walking with their children and told how finding -- or placing -- geocaches gave their outdoors adventures both a theme and destination. If your range is fairly limited and all the geocaches in an area are already "found", then checking and maintaining your own can still bring life to a stale area.
Yes, of course there will be some hassle and logistical problems along the way, but they can all be overcome and you'll be building a lifetime of memories together and infusing the children with a sense of can-do independence, a love of the outdoors, and Adventure to last them the res of their days. Can't think of a better family activity!
Best,
Dan.