I'm not a teacher. Please correct me if I am wrong. I wish we'd had... I wish we had had... You are talking about something that happened in the past before another thing that also happened in the past. I wish we'd had time to talk before I left yesterday. I wish we'd have... I wish we would have... You are talking about something that didn't happen. I wish we would have talked more about it, but we didn't. However, never we'd have like "we would had" or "we had have". Just wrong grammar.

Had. I wish we had had. It's using the past perfect tense of have.

Try them both, and it should be obvious: We HAD had more time = past perfect We WOULD had more time = incorrect; doesn't make any sense. I realize it's a bit confusing, as WE WOULD HAVE HAD MORE TIME is also correct.

"Would" is always followed by the bare infinitive. The same goes for all the "modal auxiliaries". No exceptions. So you can tell me, is the helping verb "would", or "had"?

Yes English is strange at times. 🤣