This is still a relevant question, I missed replied sooner.
You do need to reserve a FREE ticket for your 16 year old. Even though they qualify for the free ticket, the fact that you're both skipping the line makes you enter through a whole separate entrance and, therefore, to make her enter with you, you need to pay the booking fee associated with advance tickets. Doesn't make sense, but that's how the system has worked.
The whole museum is undergoing and gone many changes over the last year, so I hope that with the re-opening and return of more visitors the entire system of tickets will get streamlined.