I never used a sleeping pad until I was in my 30's, including temps down to 15 F in a 30 F-rated bag (in all of my layers, shivering ). Pads are nice.

My kids won't stay on their pad either. Straps or bungees actually made things worse because they'd roll, the pad would go to the side, and it would stay there or on top all night due to being held in place. I suspect a bag with a pad pocket like a Big Agnes would have the same result.

If it's below 60 F, they sleep in a fleece jacket, plus a fleece hat if below 50 F. (I do the same with my quilt. ;)) This allows them to stay somewhat warm no matter where they end up.