Outdoor "mudroom" to prevent cat from door-dashing?

I have no idea to help with a cat issue, don't have a barn, but that is just me. My brother but a Add-A-Room on his camper thinking his little dogs could use it. Dogs can work a zipper.
I spend most of my sitting time outside, but DW prefers inside. We hang a quilt over the door, and leave it open. Tie a leash to the step long enough for dog to get where she wants inside, or come out at will. The quilt keeps most of heat/AC in...