Drive over to Ennerdale and starting at Bowness Knott car park you can ride up to Black Sail YHA and down the other side of the valley (may be a bit far though – in which case, cross the valley to the west side and see how far you get)
Drive over Whinlatter to Lorton, then Loweswater and you can ride round Loweswater. There are a couple of disused fell roads (Whin Fell) too between Loweswater and Lorton – they involve biggish climbs, but totally traffic free.
Good ride from Lorton is to follow the Hope Beck road (find Lorton Church on the map and follow the minor road SEish across a X roads in High Lorton) This road meets a gated road leading down from Whinlatter, at Hopebeck. Keep following the road down, to join the main valley road (still slow and quiet), turn Left, then L again climbing up towards Buttermere. After about a mile of climbing you'll reach Lanthwaite Green and a cattle grid – about 150m before the cattle grid is a BW leading into Lanthwaite Woods – nice descent (with one trailer dodgy rocky drop!) to small car park at the bridge on the main valley road. From here, either turn right to pick up your outbound route, or left (towards the Kirkstile Inn and it's beautiful homebrews and beer garden). Turn R either just before the turn to the pub, or just after and pick up the C2C route through Thackthwaite, bcak to Lorton.
From Keswick, head through Portinscale and ride th well surfaced and vista laden BW along the flanks of Cat Bells, to Grange – can continue along the river past campsite (Hollins or Hollows Farm). Nice river beach to mess about on (while Dad continues riding up the BW past Castle Crag for the rockfest descent back down again??). This ride is your best off road option, but you'll struggle to get the trailer down the last section of the Cat Bells BW (behind a wood, just before reaching the road 1km short of Grange.