[villagetinker]

IMHO, your first mistake will be to have an unattended door from the birdcage to the outside. (If I have misunderstood your intent, please disregard the rest of this post, if not please read carefully.) We have predators here. We have cats, and never let them outside unless there are in our arms. They can enjoy the lanai and birdcage behind pet screen and be safe. I believe the same would hold for dogs, please be very careful. Also, your pet door will allow various animals access to your house, snakes and various other animals that I am sure will be mentioned in additional comments may enter your house.