I live in San Francisco and have family in LA so I usually ride from SF to LA every year to visit. I have written up two journals on these trips which have lots of pictures so you can see what various parts of the route look like:
journal of 2004 trip SF to LA and
journal of 2009 trip SF to LA.
While there are campgrounds along the route, you will need to inquire if they can handle the group size you will be touring with. Some of the places that have hiker/biker sites often have limited space. For non-hiker/biker sites or if using a SAG wagon, you would certainly need reservations.
While much of Highway 1 south of Big Sur has decent shoulders, as a rule, there are no shoulders on Highway 1 from Carmel to Big Sur.
North of Santa Barbara you will be on Highway 101, which in that section is a freeway. It has a wide shoulder but the cars and trucks are zooming by. Also, there are a few bridges along there that are quite narrow and need to be navigated with caution.
How many miles do you think the boys can handle? While there is lots of camping on the coast, it isn't evenly spaced. Campsites I am aware of:
Big Sur:
Pfeiffer Big Sur (showers and food), Lime Kiln (showers), Kirk Creek (no showers)
San Simeon State Beach
Morro Bay State Beach
Oceano State Beach (just south of Pismo Beach)
County park in Lompoc
Three campgrounds north of Santa Barbara
Carpinteria State Beach south of Santa Barbara
There may be others but these are the ones I recall off the top of my head.
Have a great time!
Ray