Obviously your goal is to develop a closer relationship with your daughter as opposed to driving her away, but your actions aren't in line with your goal, in my humble opinion.
I know you're angry and hurt that she left--I would be heartbroken if my daughter did the same thing to me--but your anger is only increasing the wedge she's created between you.
Instead of threatening or harassing her over the charge, why don't you call the credit card company, close the account, and have them issue you a new card with a new account number? That way, your daughter can no longer charge items to your account and this issue won't get in the way of your attempts to resolve the real issue:
Developing a closer relationship with your daughter.
So how can you do that? Call her and ask her to have lunch with you, invite her over to your home for dinner and a movie, ask her if she'd like to browse through a bookstore or an antique shop with you or play a game of tennis, etc. You get the idea. I think her behavior is screaming "Mom, I need some special attention." And you know what? So do you. Wouldn't it be nice if the two of you could pamper yourselves together?
I think it will do wonders for both of you.