, I wasn't suggesting that the OP's cat was chasing the cat out of fear/anxiety since I haven't seen the animals interactions. Rather I was explaining what was going on with my dog and cat.
And honestly for a while in the beginning I wasn't sure if my dog would hurt my cat bc sometimes, well, a heightened dog is a heightened dog. I didn't want my cat or dog to live like that so I started working hard on the counter conditioning with both of them.
But---I was offering some suggestions that may help AS she is working on training her dog to relax in the presence of her cat. If you go back and read my post I said that I used counter conditioning with my dog on a leash
to change her mindset about how to interact around our cat. And the high shelves can really help. If the OP keeps her dog on a leash in the living room, for example, in front of the cat on the high shelf, it can really help the situation. The cat will feel safe up high, and the Op can give her dog treats and praise for relaxing in the cat's presence.
I also baby gated off one room all the time in the house for our cat to retreat to. When I got home everyday Gracie dog and I would go "visit" Tortie cat at her gate. I always used the same phrases of "Let's go see Tortie" or "Gracie, where's Tortie?"
I made it a quiet
happy game, with asking Gracie (on leash!) to lie down in front of baby gate and I gave both Tortie and Gracie treats. Eventually she got so used to the training game that she would come home and look for Tortie before even saying hi to her Dad, my sig other, who she looooves.
This worked wonders for us, so it may help the Op to train the dog not to chase the cat.
I also used this same training method to teach my dogs to be able to watch birds up close, squirrels, babies, etc.and not chase them.
And I agree, letting the dog chase the cat is dangerous and super stressful!! Separate them until the dog is no longer a threat to the cat. Baby gates, leashes, etc can help.
Hope this clarifies my prior post. Thanks