BAH terms don’t state that all passengers must be adults. They state
5.8. The person who makes or pays for the booking must be at least 18 years old. Some hotels and other suppliers may require some or all of your group to be at least a particular age, or for at least one person in each room to be of at least a particular age. The majority of hotels in the USA for example impose a limit of 21 years old. To check a specific hotel’s policy, please contact us.
I read the OP before it was edited, the situation is a little more convoluted than it now reads, but I will leave it to the OP to decide if they wish to disclose that.
OP - there is unlikely to be any issue per se with taking the flight and not using the hotel, if you can get BAH to accept the booking in your situation.