How does it work when you recover a shield but have to turn a damage card up, but that ends up being a pilot trait crit. Can you discard that card through the Determination EPT?

Nope. Determination only triggers when the damage card is dealt face-up. R2 doesn't count.

Determination, and Chewbacca, work when being DEALT a face-up damage card. If you've already been dealt the card face-down then it slips by those things and can later be turned face-up with interacting with them.