I just recently adopted a stray kitten and it had learned to use the litter box, but?

I still dont trust her yet because she somtimes randomly urinates outside the litterbox. I've come to a compromise which i dont know if its cruel or not. Basically my plan is to put my kitten in a fairly large clean garage with its own set of bowls for food & water and its own litter box, whenever I go to sleep or go out. The reason I decided on the garage is because if I lock her inside a bedroom size room or bathroom, she will start crying and and puting its little paws underneath the door. But whenever I put it in the garage it seems that she doesn't mind it becuase like i said its fairly big. Do you think this is to harsh and cruel for the little kitty or is this a reasonable compromise?