Cycling/exercising as a family is fun for everyone, I highly recommend it. Before my kids turned 3 they rode Strider balance bikes, so I walked/jogged with them. Around the age of three and a half I started cycling with them ( they rode a pedal bike ). However they were small and tired fast ( kids love to trying to race at the beginning, which tires them out super fast ) so it was easy to bike with them. Our normal rides would last about ten minutes on flat terrain. When my kids turned 4 & 6 they got stronger so we had to change our routine, they were able to ride for 20-30 minutes and they could handle moderate hills. Small hills are a great challenge for developing children ( no big climbs ). No one likes to walk up hills, so we created a unique group solution for our family. On hills that were too much for the little ones, I would get behind, grab their shirt and hold it while I peddle up the hill. Doing so lets me pull them up the hill safely, and it allowed them to pedal which helped me . After I got the first up I went back down for the second child ( always changing the order that I bring them up...you can never bring one child up first on consecutive hills ). It took a about a year for the kids to get strong enough to climb on their own ( also better bikes with gears helped ). Now we go for 30-40 minute road rides or 20 minute off road rides ( off roading is much harder but more fun ).
To get your kids cycling I would encourage you start riding with them at a young age. Every family is different, but listen to them and help them when they need it. Try to get light bikes such as a micro mini for 4 year olds, and get bikes that will grow with them. My kids loved when I helped them ride up hills ( by grabbing their shirt ), try that to see if it works for your kids.