Managing cat reactivity

Hello! I'm looking for success stories, tips, advice etc on living with a cat and a high prey drive/cat reactive dog.

When we first adopted our (now 18month old) Kelpie X 6 months ago, she was interested in the cat but we kept them separate thinking they would get used to each other, slowly introduced through glass doors, pet gates. However, our dog has only gotten worse – she cries every time she sees the cat, sprints around the house to the laundry door when we sees us walk to that part of the house (where the cats food and litter are kept), and has chased the cat on the one occasion the cat ventured out of her part of the house over the pet gate. She doesn't seem to want to bite/attack, rather just wants to play/gives her a little bump with her nose which the cat doesnt appreciate.

Our house is small, and while it is manageable to keep them separate, it's still not doing anything to curb her reactions when she sees and hears the cat. And it's hard to do training when the subject is another living being (sassy cat who seems to torment the dog when she knows she can)!

I would love to see them co exist and be able to remove the pet gate that separates them. I also feel bad that the car has had her whole world shortened because we are trying to keep her safe from the dog.