It may seem too simple to work, but you just need to cut your own tailor-made cat door.
Basically, a cat can get through any opening it can fit its head through. This usually works against us cat owners, since the beasties have a mind of their own and like to explore. This time, it may work in our favor. So:
- Measure cat head (breadth), add 1/4 inch to make things easier.
- Cut opening in door about that width, of reasonable height (8" should do the trick, perhaps even less).
- Teach cat to go through the door, perhaps with some treats on the other side.
- Watch dog try to fit her wide head through the opening, fail miserably.
- Watch dog proceed to try to make opening wider by scratching.
- Patch up the sides of the opening with metal.
Hope this helps (the cat).