Just thought of something… you can try to put double sided tape on the outside where the cat would enter.. I’m not sure how well your pups would do with stepping on the tape, but if you just put it there for a little bit the cat should stop coming.
My Mom has a cat that jumps on her bathroom sink, she will mess up everything, lay in the sink, make all her items fall on the floor etc. So my Mom put double sided tape on the edge where Trixie would jump up- It took a couple times, she has stopped jumping up there!
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