Can 'which' be omitted?

Yes.

Do you mean the below is correct?
"We use..to talk about things that were ideal in the past but didn't happen."

The sentence could read, We used to talk about things in the past that were ideal but didn't happen.

It sounds a little cumbersome in that format. Another way to present the idea would be, We used to talk about things in the past that were ideal but then they didn't happen.

Thank you
The complete sentence is:
"We use should have + -ed form to talk about things that were ideal in the past but which didn't happen."