I thought I should let you know about bike rides I set up for really little kids, as the family rides run by BUGs and clubs are usually around 20km - generally too far for a 4 year old on training wheels.
They're called Mums (& Dads) on Bikes and are run under the auspices of Darebin BUG. Some people travel to come along on them. I can think of regulars from Ascot Vale and Kew and some say they come along to show their kids that cycling is a normal activity.
My rides have the motto: No one's too slow and we're happy to stop for a rest, snack, play, breastfeed, nappy change or until a tantrum is over.
The rides all go to family friendly destinations, often with a range of options (eg, ride to Melbourne Museum: museum visit, IMAX, or play in the playground, watch bike polo, picnic in the park, bike checked by Bike Fix).
To make them shorter (and to encourage multi-modal transport), we often take the train. I always have maps with me and have been able to reveal fabulous commuter routes to my unsuspecting parents.
Some of the novice parents have become more confident and competent and I've managed to encourage some to do more cycling, say by entering events. One of my neighbours now rides to the shops and has asked me to do training rides with her.
The reason I'm telling you all this is not to promote the rides (the Sunday rides are often too big as it is!) but to encourage you to consider setting up similar rides near you. Like me, you may find your kids become better cyclists (my 7 year old has done a 30km ride) and you have more people to ride with.