Oh I know exactly what you're going through! My 2yo DS is the same! Luckily he keeps his clothes on whenever we leave the house except for the other week we were at a birthday party and I looked up to see him jumping on the bouncy castle without his shorts on. Luckily he stopped there and didn't take off his nappy aswell!
Him being naked doesn't bother me except that like your DD, he's not yet toilet trained and I really don't enjoy cleaning up the wees and poos. I've tried many things and like someone suggested, I move the potty around the house so it's close to where he's doing most of his playing.
I also use size 2-3 undies which I put over the top of his nappy. They are a little harder to get off so he doesn't strip off as often and if he tries it takes him longer so I catch him in the act