I am hesitating to give a reply to your request because you know that I tend to defend and promote my lovely valley of the Chablais and Portes du Soleil area. So I don't think my suggestions would be very objective.
However if you decide to come over to this place of the Alps, then I would recommend a few resorts like Les Gets, Chatel or Samoëns. You know already Morzine. I don't recommend Avoriaz in summer.
Over here there are lots of activities to do :
hillwalking and rockclimbing
white water rafting and canyoning
cycling and mountain biking
swimming in Lake Léman or in many swimming pools
glacier walking nearby (Chamonix or Glacier 3000)
cruises on Lake Leman to visit Lausanne, Evian, Montreux, Chillion castle
many music festivals
and many more...
End ofJuly, beginning of August, the summer weather is generally good and settled (but it depends, sometimes we get rain and snow on the moutains).
The only problem is that the first weeks of August are very busy everywhere with tourists from all over the world, especially in famous resorts. But still you can find some quiet places far away from trendy resorts.
I could recommend some very peaceful and beautiful resorts (and also cheaper) :
Bellevaux and Vallée du Brevon (that's the valley where I live),
Vallée d'Aulps (that's also the valley where I live), highly recommended.
Abondance and its valley.
The smallest resorts on the last three links are not as busy as Les Gets or Samoëns and they are also cheaper as regards accomodation. They are close to the main places and if you have a car, it will be easy to drive anywhere you want to go.
Another bonus, if you come over to the Chablais and Portes du Soleil, I am sure I will have some time to guide you and your family to some nice mountain places, for example our old mountain chalet I know and you'll taste again our home-made cider or home-made Eau de Vie (local whisky). Cheers !