If you rent space in someone else's kitchen or a church kitchen, how do you store your partially completed cakes? Does your rent include storage in a freezer for frozen cakes, a fridge or a storage place.....or are you allowed to take them home for storage as long as no baking is done off site?
It should supply some kind of cake storage not to mention storage of supplies and equipment.
No, you cannot abide within the health department guidelines and bring stuff home--that's the point of doing it elsewhere. It's not just the literal baking--it's all of it.