when our kids were smaller,we found it easier for them to use dollars, and just gave them so many dollars a day to use. with travellers cheques sometimes you are asked for i.d. so that means having to carry that around as well.
We don't bother. We just note how much spending money they have and either use our credit card, cash or travellor's cheques and just take it off when we get back to the hotel.
At 17 she could just as easily have her own TC's and use them as cash, getting cash as change. That way she will have the responsibilty of budgeting for herself.
I'm taking my 12 yr old niece with me in September - and her mum is getting her $250 in travellers chq's, $200 in cash dollars and 50 quid in english money in case she runs out.