I don't know if you noticed, but you also can't cook in additional homes as long as you're only visiting.
Actually you can cook in your additional home as well, but
only if you click on the stove. Both the ordinary type, and the other ones from Store, Teppanyaki and Wood Fired Oven works fine, just like they do in your normal home. It's true that none of the easels work, but that other big sketching table does, so if your sim wants to practice painting in his/her additional home, and have the space and money, you can buy and use one of those instead.
And about your sim not being able to move to your additional home, have you tried letting your sim use his/her own car or bike, instead of the taxi? I tried it recently a couple of times back and forth with my sim driving her own car every time, and that went all well.