So I never actually got to send my email to the parent (I was trying to track down my administrator to clear it with her), because before I managed to sit down with my admin, the parent apologized. She said she'd been stressed with everything her family was going through but hadn't meant to be so rude and was sorry, and thanked me for everything I've been trying to do to help her son.
Her son still didn't have a pencil on Friday, but he did turn in the missing major assignment, and he's at least passing now (I'm assuming - haven't actually graded it yet).
So. There we go. Still not the most pleasant moment of my life when I read her first email, but I'm pretty impressed that she actually made the effort to make it right. Not enough of us apologize when we mess up; doing so goes a long way with me.