I think this may help you:
It allows you to create an Apple ID without a credit card, so that your daughter can only get Free Apps, and nothing else. It is used for students.
You may also consider (and this is purely advice, of course I know nothing about your beliefs or child raising philosophies) a reloadable debit card, which she can use with the account to buy songs or purchase apps. My bank gives me a "Teenager Debit Card" which my daughters have. It has a locked amount of funds on it (basically their allowance), and it's used on their iTunes account, or whatever they want. I actually have control as to where they can spend the money (no fast food for example).
I think that may work for you. Because not only are her messages coming to your devices, but technically, she could read your messages. That happened to me with my daughters recently, when my ex set up my daughter's phone wrong, and I sent my ex a message that my daughters read. Not a pleasant situation.