Settled on a custom order vinyl screen door with large pet entry from Office Depot. All hardware is extra.
Just word of caution. The advertising glib about using tools that you would use on wood are true on this door. I trimmed a 1/4" off one side for proper fit in opening with a circular saw. That worked fine. I decided I wanted the edge I just cut to be rounded over just like the other outer edges of the door. Using a hand held router and 1/4" round over bit, I attempted to recreate that on the freshly cut side. The straight part of the router bit (guide) tends to bury itself in the vinyl. Did manage to complete the round over after learning that hard lesson. Just had to do it tenderly.
Now, if I can only get the dogs to enter/exit through the pet entry...