I use a doggy door that goes out to my enclosed porch with a pad and I tell you that is the best thing! You could use an ex pen on the other side of the cat door for an enclosed area. My new pup is almost 10 weeks and is not big enough to open the door yet but I can't wait till he is! We have a medium dog door. I really think it is easier to train once they know they can go in and out on their own.
