How to properly introduce pets who had a run-in in the past?

Alright, so I have a cat and my girlfriend has a smaller dog. (It should be noted that we don't live together) The dog is barely larger than the cat and is also very hyper. The cat just wants to chill, especially when the dog is around.

When she first brought the dog around, the cat was just curious and maybe a bit cautious of the dog, but if it could be on higher ground and silently watch the dog, it was ok. The dog would eventually spot the cat and chase it. The cat would escape, but eventually come out and let more of its curiosity get the better of it.

Then, my parents visited with their dog. Their dog, also a smaller breed, is much more "chill" than my girlfriend's dog. He and the cat were found napping on the couch side by side a few times. No issue co-existing. But, like any puppy, this dog likes to play and really had a ball with my girlfriend's dog. So, one day my girlfriend's dog, while playing with my parent's dog, noticed my cat and gave chase. My parent's dog gave chase to the girlfriend's dog (based on their interaction prior to this moment, I'm assuming he was not chasing the cat), but of course the cat didn't see it like that.

I found my cat on a window sill with an arched back, hair on end, clearly very shaken. He hid in my room all night after that. Ever since then, and it has been a while, whenever my girlfriend brings her dog over, my cat has no curiousity, he is in hiding, period. And when cornered, there is hissing. It should also be noted that my cat can still coexist with my parent's dog, despite its "involvement" in the incident.

With the plan of eventually living together, we are trying to get our pets used to each other. Part of it is getting the dog to settle down as that is one reason I think my cat is on edge. But the other part is getting the cat to "forgive and forget" that incident, as he seems to remember it.

Any ideas?

Thanks