Hello kokonutz,
I can't speak to if it would be better to get a card in your name, since my Chase Sapphire Preferred app was (rather quickly!) accepted when I applied. However, I'm a college student myself, who is currently studying abroad in the UK, and got the Chase Sapphire Preferred card exactly because it has no foreign transaction fees. I'd highly recommend it so far, it has worked flawlessly since I arrived in the UK about a month ago, and not having a "chip" feature is no problem so far, everywhere that takes credit cards has taken mine without an issue. As a plus, the customer service with the card has been nothing short of exemplary! I'd say it's definitely worth having your daughter give Chase a call and see if they will issue her a Sapphire Preferred card in her name.
Hope this helps!
-NWARJ