Nick, the route to linderette is in the the bluerun on the map or another track?
No. It crosses the blue but should be marked orange (ppds). Actually thinking about it going all the way back to Morzine from there is quite a ride for little legs so do it early if you fancy it. One cheaper way to do it is drive to Avoriaz, ride to Morzine (no lifts) then either you get the bus/lift to Avoriaz using the multipass to collect the car or you all get the lift on foot, go to the ace swimming pool in Avoriaz then drive home.
Along the river to Morzine sounds good.
For a very easy ride you can just ride out and back along the river path. Its quite pleasant and a flat ride.
One more easy, nice one on a sunny day is part of the big ride above. Drive to either Lac Mondrian or the ski lift above it. Ride to the lake, play on the beach, paddle, etc, carry on to Morzine via the river then later in the day bus or road bike back to collect the car.