Can my child miss part of the tournament?

Yes. At any USCF tournament you can request a "bye" for any round. Usually players do this for scheduling reasons like if a player has a piano recital at 7pm and the tournament begins at 4:30pm, they can schedule it so they don't have to play the last round. Just make sure to let the tournament director know before the tournament starts. Also once you request the bye and the tournament has started you can't change your mind.