No kidding, it\’s possible to ride safely with young children. I admit I have no personal experience with this, but the Internet has a lot of information on the subject.
I\’m not speaking here of youngsters old enough to ride their own bicycles; I mean kids between, say, ages one and three. The child should be able to hold up his head, and the neck needs to be strong enough to support the weight of a helmet; this begins at about one year of age.
So, how do take the very young child cycling? One option is a bicycle trailer. Put a helmet on her; strap her in; hitch the trailer to your bike and pedal away. An advantage to this mode of child transport is that other items can also be stowed in the trailer; and when the child outgrows it, the trailer is great for bringing home the groceries.
Another possibility is an over-the-rear-wheel seat. I\’ve seen bicycles equipped with these. It seems to me that it would take quite some practice to be able to control a bicycle with a weight up to 40 pounds behind you. This would be very different from having a load from the supermarket back there! Groceries might get heavy, but at least they\’re inert. Children move!
Maybe your child can be your co-pilot: helping you with hand signals, for example. That would let the youngster learn some aspects of cycling before he or she starts to ride independently. Then the child will have a good start on a lifetime of cycling — no kidding!