Can I give my 15 yrs old my card when she goes travelling?
Yes, but you are fully responsible for anything that happens.
I suppose the answer is - who will know?
They will have every right to deny a dispute (chargeback) from you as they will have solid evidence against you.
I mean they will follow through with the process but could decide in the merchants favour. Read the T&Cs carefully.
Make sure to disable location based security!