For the cat/dog problem. We solved it by DH making a half door, sometimes called a Dutch door, out of pegboard. The doggie can look through the holes and see me. The cat jumps over the sill and can come in the room. If making one from scratch sounds too intimidating, cut a hollow door in half and place a shelf on top for kitty to perch. It would already be prepared for the hinges. It really works for us.