Replying to myself:
The simple semicolon and the word "then" make me think that you resolve the Stunning completely before you draw the card.
Lose 1 life.
If this makes you stunned, do all the discarding.
draw 2 cards.
Otherwise it would have been a lot clearer to say "Draw 2 cards; then lose 1 life".
You are correct. Resolve being Stunned, then draw two cards.
Game Designer - USAopoly