Looks like a great trip. You may run into some availability issues especially on the long weekend (July 1-3). I'd recommend booking sites as soon as you can, especially if you want to be in some of the more popular campgrounds.
Here are a few quick recommendations:
Radium - campgrounds: Canyon RV Resort (private), Redstreak Nat Park. Radium Hotsprings and Invermere are the attractions here, but I assume you already know that because Radium is one of your destinations.
Fairmont - campgrounds: Fairmont RV Resort and Spruce Grove Campground. Both ok, but you can walk to the hotsprings from the RV Resort.
Kimberly/Cranbrook - Campgrounds: Kimberly Riverside Resort (has a pool and mini-golf), Wasa Lake and Moyie Lake (BC Prov Park campgrounds). Fort Steele is a good attraction in this area.
Cranbrook-Rock Creek : I don't know any good campgrounds in this area. You might want to consider a detour through Balfour and Nelson instead of the south route you have. If you do this, Ainsworth Hot Springs is just north of Nelson. This is probably the best hot springs we have been to as there is a large horseshoe shaped cave that is part of the hot springs.
Rock Creek - Kelowna : Lots to see and do here. The Okanagan can be particularly busy at this time of the year. There is an ok campground (Todd's RV) in Peachland that is right across the road from the lake. The traffic through Kelowna is ridiculous so account for that if you want to do much around there. Check out the Myra Canyon trestles, an abandoned railway that has been converted into a hiking/biking trail. Lots of wineries in this area too.
Kelowna-Sicamous : Lots of campgrounds, some of which are right on the various lakes. Dutch's in Vernon is very close to Kalamalka Beach, but the campground has very mixed reviews. The beach is beautiful though.
If you let us know where your route ends up, I'd be happy to give more specific hints. We also have a 10 year old daughter, and if you tell us what type of activities you like, I'm sure there will be lots of good input.
Again, this looks like a great trip.