Round Ladybower / Derwent / Howden reservoirs is nice with the kids – it’s about 12 miles I think. Nothing properly steep, but a couple of slopes that your eldest will prob need to walk. Easy surface. Nothing there on the way round, but there’s a cafe at Fairholmes.
Granted when I did it with mine of a similar size it was the worst ride in history [seriously, my kids remember it to this day] – the rain and wind came in and we were sheltering under the bridge at slippery stones like refugees. But if the weather is nice it’s a pleasant spin.
Aside from that you’ve got the old railway lines which are nice with the family. Monsal trail, Tissington trail.