As I moved down to the Branson area this past may, I find it a very interesting city to live near. Yes there is alot of traffic but thats true with any tourest area. Alot depends on the age of your kids. There are many family activities to do while in Branson. I think Branson is the gokart and mini golf capital of the world.
Anyway as for camping there are three lakes Table Rock, Taneycomo, and Bullshoals. Table rock closer to Branson Taneycome down stream and Bullshoals further down streem. As for kayaks the last two lakes would be better for. Most of the RV parks in the Branson Area proper are not by or on the lake. Table Rock lake state park is a good one. About one hour drive from Branson is River Run campground, its a COE park on Bull Shoals lake. There is so much to do in Branson I would look into the RV parks in the area. Wilderness Campground is tied to Silvar Dollar city. The sites are tight (but then all here are) however they have a shuttle to Silvar Dollar City.
Good Luck and Enjoy Branson