English Translation
She could play the piano.
Podía is the imperfect form and podría is the conditional form. I think it’s difficult to plainly translate to English, as it would be the same translation for both forms, but they do have different meanings. So I guess “podía haber ido” means something like “was able to have gone” and “podría haber ido” means something like “would be able to have gone”. You would use podía if talking about a situation that happened in the past, and you would use podría if talking about hypothetical situations or probability.