How do I dog proof a glass storm door with a push latch on either side and still be able to use the door?
I'm not sure if you mean "dog proofing" meaning he can't damage the glass, or he can't get out.
You could put a protective film over the glass so the dog can't damage it.
You could install a doggy door within the door.
Thank you everyone for the suggestions! I ended up buying a new Strike Plate which has been great! It holds the door firmly in place and the dog jumping on the door isn't a problem any more!
Purchase a baby proof sliding door latch?