To add some additional advice on activities with children.
There are various kids clubs in Verbier. Some are residential, some are day camps. There is quite a difference. If you are there with your own children (as we have been), I would avoid the residential camps (e.g. Les Elfs). It's just my perspective, but groups seem to be a mix of rich kids from around the globe with the look of "ennui" that can go with that. There are some great day tennis camps, biking instructors, riding camps, golf instructors etc. Personally, I tend toward specialising by activity (one week x, the next y). There are some mixed activity camps, but one of the great things about Verbier is the strength of coaching from specialists who are passionate about their activity. All are very child orientated. The Verbier music festival also has a strong childrens programme.
You can get all the details from the main Verbier website or contacting the tourist office. It's impossible to lay out in a post all the possibilities - a long summer rental with children sounds like a wonderful way to pass the summer.