Doggie doors are installed only on one door. So a storm door with an interior door will not work. Have you thought about doing a doggie door in the wall?
Lowes stocks an aluminum screen/storm door with a built in/on doggie door. It retails for about $225 in the metro Atlanta area.
As stated above, you have to leave the interior door open for the puppy to return
To eliminate the problem of having several unwanted cats coming inside their house during the winter. our friends installed a pet door that only opened for their animal by using an interacting collar. New one on me.
i"m having enough trouble with a smartphone let alone door like that...lol
We recently installed a Patio Pacific Door with Endura Flap. My 6 lb. guy is having trouble pushing the door open because the magnet is super strong. I put some masking tape over the magnet to soften up the attraction and we are working on coaxing him through.