Forest of Dean Family Cycle Trail
The Forest of Dean has plenty of options for cyclists: in fact, the traffic going past Tibberton Cottage on a Sunday morning is most likely to be groups of road cyclists. Forestry England run Cannop Cycle Centre in the heart of the forest, and from there you can ride a blue trail, red trail, or the family cycle trail. Like lots of people, we take our own bikes, though you can hire them from pedalabikeaway (booking advised).
With young children, the only one we've tackled recently is the family cycle trail, or some of the tag-on sections. We have a slight preference to start the trail at Cannop Ponds, which is a little bit quieter and directly on the family cycle trail, as opposed to the Cycle Centre or Beechenhurst which are 100m or so off the trail. The trail itself is 14.5km and will take the average family about 3 hours to do. We normally take a picnic and make a day of it.
Do be aware that the first part of the trail is deceptively uphill; it doesn't look it, but there's a slight gradient on the dismantled railway, and it can make you feel very unfit if you aren't aware it's not level. Rest assured, you get to profit from all that hardwork later on.