Thanks for the well wishes, all. It's a dent and a scratch, and the car isn't wrapped. It looks deep enough that I really don't think a wrap would have saved it, though it might have been a little better. We'll see what the body shop says about how it needs to be fixed.
I've never had my kids open a traditional door into another object, so this is new to me. I've been clear with my son that it's not his fault, since he couldn't see what was behind and above him when opening the door (a traditional door would have opened past the pole without a problem - it was the sign on top that caused the issue).
The lesson, really, is just to be careful when parallel parking, and observe what's next to the space. Just because every other car on the road can open its door safely doesn't mean the X can. It's one more nuance to the ongoing ingress and egress conversation required with your passengers. The main phrase you need to learn is "I've got the doors, don't touch them."