I'm not sure how strong a greenhouse frame would be, the taller the cage you make the more sturdy the frame needs to be, which is why cages are normally made with steel or iron. Also is aluminum painted or coated with anything? Any kind of paint other then powder coating, like the use on cages and wheels, is not safe. Another issue I see is if the chin chews on the aluminum, aluminum is a soft metal, and chins can, and although rarely, have chew though aluminum running wheels and scatter guards if they put their mind to it. If it's a thick heavy aluminum frame that is just aluminum not painted or anything it might work.
Wood can work, but it's not really advised. Again keep in mind that the chin will likely chew it, and if they pee on it it can be hard to clean the pee off, shelves you can spray down and sand down to remove pee stains, and even replaced if the stains are bad, but a cage would be hard to do that. As well as if the chin ever gets a fungal infection all wood, including the cage itself it made of wood, will need to be thrown away. If you are ok just building a new cage every few years that can work, but it wouldn't be cheap unless you have access to cheap lumber.