I guess I don't have as much to contribute as I thought. We incorporated biking into our annual camping trips, so camping also meant meant. We did also do regular rides on paved trails from home. Like any family day together we made it as interesting and fun as possible. What the kids learned over time was some core values about "family". I think if you emphasize the "family" aspect they will look at the activity as an integral part of their lives. I would suggest not pushing them, meaning, be sensitive to their limits. My limits are much higher and so my expectations for my ride were tempered by the fact that I was spending time with my family. When I want to really book, I ride alone. Also work in rewards if you can. Scenic area? Beach? Ice cream? Other goals worked for us too, such as biking to see grandparents. I also keep track of mileage and speed and the kids were always impressed and proud of the miles they racked up and interested in their speed. Be sure not to brag about your own stats when riding solo.
The other thing I did was bought only used bikes (w one exception) because kids grow and so do their bikes. Their must have been 5 bikes for each kid (total 10 for 2 kids) over the years before we finally landed them on adult sized bikes. The most use we ever got out of any of the bikes was 2 years. Beyond that you're pushing it, meaning the fit.
Enjoy! :-)