I am trying to think of how the dogs could get in and out without some sort of flap.

There are hard plastic pet doors. I got mine at Loewes years ago custom made for around 80 bucks. Easiest install ever.

About 15 years ago, I installed a Solo Pet Door for my cat (to keep raccoons from getting in the house). I am completely satisfied. The door opens with a magnet on the cat's collar and raccoons cannot pry it open.

In all this time, I have had to replace a small metal piece once and the cord twice. Neither was expensive or difficult.

Customer service has been excellent. A couple of years ago, the door became completely inoperable. I thought the motor died and called the company for a replacement. An incredibly kind man suggested I reset the breaker. Problem solved! This shows how thoroughly inept one can be and still maintain the system.

It isn't an inexpensive solution, but it has been worth every penny for me.

https://www.solopetdoors.com