You draw a card and discard a card all while The Royal Scions's first ability is resolving. Nothing can happen between the two, and no player may choose to take actions.

The Royal Scions's last ability goes on the stack without a target. While that ability is resolving, you draw four cards. When you do, the reflexive triggered ability triggers and you pick a target to be dealt damage. This is different from effects that say “If you do . . .” in that you choose a target after looking at the cards you draw.

If you draw fewer than four cards while resolving the last ability of The Royal Scions, its reflexive triggered ability doesn't trigger.

If replacement effects cause you to draw five or more cards while resolving the last ability of The Royal Scions, its reflexive triggered ability still triggers only once, even if you draw eight cards.