According to Google Maps the most direct route from Spokane to 100 Mile House would take you through Osoyoos, Summerland, Merritt, Kamloops.
I don't know of any rest stops on the route that allow overnight camping. My suggestion would be to spend one night in either Haynes Point Provincial Park (near Osoyoos) or Okanagan Lake Provincial Park (near Summerland). Reservations in BC open at the beginning of March and you should make your reservations as early as you can if you intend to travel in the summer.
Here are some photos of Haynes Point and Okanagan Lake Provincial parks. There are no services at either of these parks, but you can fill your tank with fresh water.
Okanagan Lake Campsite Sept 2013 - a set on Flickr
Haynes Point June 2013 - a set on Flickr
You can contact the Walmart stores in Penticton or Kelowna to see whether overnight camping is allowed. I would recommend staying at one of the parks instead.