Poppet, out of curiosity, could there be some kind of hidden back entrance in the yoga studio, or more likely an open back door? If you don't answer while I finish up the post, I'll go with open back door scenario. :D
Question: are there any fences around the yoga studio, anything at all or they can just drive up there during this time and sneak in some building or something?
Oh my. Well, I've not had a kitten, but I have a devil of a cat. I'm sure that the one you found would have nothing on mine, so, I'd like to encourage you to keep it, but that's your and your family's decision. Any pet is responsibility and as you mentioned, furniture and the like does matter. S/he might be content with scratching post, though? XD;