Wow, thanks for all the great comments!
I used fusible fleece for the backing of the clothes and it seems to stick fairly well. I didn't quilt inside the squares because I didn't know if it would make it harder to stick to.
The quilt was hanging up when I took the picture and the clothes stayed on really good. I figure the kids will lay it out on the floor to play with it anyway, that's what I was doing when I was playing with it LOL!