the exact relationship between Cooper and Diane?
Cooper and Diane don't seem to be in a romantic relationship during the original show.
But they are close friends. Maybe they were in the talking phase before one decides to date someone? Or perhaps, they've always just been friends.
I think Diane did friend zone Cooper during the events of the original show, and Cooper had this massive crush on her. That's why Cooper did have a brief relationship with Annie. Cooper also said in season 1 that he was single.
In Part 17, you could interpret the reunion kiss and embrace between Cooper and Diane under a "just friend" lens, perhaps. Diane was very overly joyous to come out of the "prison" she's been in the last 25 years and Cooper is the first person she sees. Since Diane just sees Cooper as a friend, that's why the sex makes her feel uncomfortable in Part 18.
Janey-E shows far more sexual/romantic attraction to Cooper than Diane does. Diane leaves Cooper in Part 18, while Janey-E did not want Cooper to leave her.