I think the game really needs to do some stuff to make puppets work better. You should be able to indicate, in some fashion, what buildings a puppet should build (culture, science, etc) -- or the puppet should at least not make buildings so that it requires more money than it is giving. I think ideally you indicate whether it should do culture, money, or science, and then it tries to build those sorts of buildings, maintain a neutral economy (or positive for money), and be neutral in regards to happiness (build enough happiness buildings to cancel out its own effect on unhappiness).

Also, I think you should be able to found a puppet city. If there is a luxury, strategic, or other resource you need, then you should just be able to put a puppet city down there. I don't think that's unreasonable and would help flesh the game out a bit. I guess if there was some other way to claim territory and such short of a great artist, then that might work too.

I know there'd perhaps be some balance issues here, but nothing that I think couldn't be resolved.

Edit: I realize telling them to build culture would probably be OP, so that shouldn't be an option unless there's something to balance that out. IMHO, puppets are a nice concept that needs a lot of tweaking.