Well, given that most of us on this forum live in the area - we of course think yes! The whole area is dubbed "nappy valley" precisely because so many people with children (all ages) live here.
There are many "sub-areas" in the wide area, it all depends on your budget. "Between the commons" (abbreviated as BTC) is the area between Wandsworth and Clapham Common which would be very close to Thames Christian College, is just off Northcote road, and is in close proximity to Clapham Junction if you commute into London (if you happen to be more on the northern side of it, then Clapham Common or Clapham North stations might also be an option). Slightly cheaper properties will be around Lavender Hill. It might boil down to what accommodation is available at the time you are looking to move.
My children are very young so can't give you advice on things to do with older children, but I am sure other people on the forum can.