How would this sequence of effects work? My interpretation is that if a ship with XX-9 Turbolasers hits an enemy ship, inflicting a critical effect and scoring at least 2 damage past shields then they can be in for a world of hurt if Dodanna is in command. It seems that the Rebel player would examine the first 4 cards, place their choice on top and put the other 3 on the bottom of the damage deck. Then repeat the same procedure for the second critical effect card. This makes a nasty combo if you are able to score the damage.

Do I have my head wrapped around this correctly?

Yep. Pick out of 4 for the first, then pick out of 4 for the second. Technically the cards are discarded, though. not put on the bottom of the deck.

Oops, yes discarded. Too many rules for too many games rattling around in this old brain of mine.