I've been working on this one for a while. They said it couldn't be done (the voices in my head, that is), but I've proved them wrong. So here it is - the family-friendly route from Upper Norwood / Thornton Heath to Richmond Park - in just under ten miles.
Distance is just under ten miles each way - but as the route is a bit wiggly & there's a significant hill just after Wimbledon, you'll want to allow 1h15 to 1h30 each way. Stop for a snack at Figges Marsh or the Wandle Trail. The whole thing is a 20 miler with some hills so age wise this is probably a 9+.
On the return trip, you may be better off taking the "allotment path" out of Norbury Park (bear right after the BMX track) & heading up Virginia Road. Norbury Hill has a fair bit of traffic and when you're going uphill it's not great.
There's a railway footbridge at Mitcham so no cargo bikes on this one, sorry. (You can use the level crossing at Mitcham Eastfields instead, but it means a couple of hundred metres of Grove Road & the busy roundabout at the end. - not ideal with kids. There's an alternative to go down Acacia Road past the BMX club and back up again, but it adds another half a km on to a ride that's already quite long).
This route recommends a very short dismount (sub 200 metres) to get across the railway at Wimbledon Town Centre. There's a route further south on mostly quiet roads, but that requires a second railway footbridge, you end up dismounting either way so this is easier. It's either that or go the long way around their nasty 1980s one way system. (The 80s: Great for music. Awful for town planning.)
The surface on Wimbledon Common is kind of rough in places and may be muddy at times - don't bring your shiny £2k road bike or wear your sunday best!