Find a lesson to learn from it so that you can improve your service moving forward.
Perhaps you need to change your processing times, so that it gives you more leeway time-wise when you need to order in supplies.
Or keep more supplies on hand so this doesn't happen.
If it's not ready to ship, you may want to change it to "made to order", even if it still has a shorter turn around time. She was definitely upset about the delay in shipping. So you have several ways you could improve that area.
As for the actual product.... from reading her comment as well as yours, it sounded like one pin was made with your original batch of rhinestones, and the second pin was made with the new supplies. And they didn't match. If you're selling a PAIR of hair pins, I would also have been upset to get a pair that didn't match. And a half a refund would have felt like an insult as well. Because if she's supposed to use them as a set, refunding for only half of it doesn't suddenly make everything all right.
I'm not trying to be mean, I'm just trying to get you to see it from her point of view. Right now, you are hurting & probably angry, so you're only looking at it from your point of view. When you're calmer, you need to try to look at it from HER point of view. She got mismatched pins, of different quality craftmanship, that were delivered later than she expected them to be.
I currently don't do any kind of marketing to brides, but I know the market can be brutal, and meeting deadlines is absolutely CRITICAL. They are running on deadlines. So if you say it's going to ship by a certain date, then it MUST ship by a certain date. Get into the practice of under-promising and over-delivering. If you think it will take one week, then give yourself two, and surprise them by shipping it sooner.
Anyway, I hope you get what I was trying to say. The best thing you can do is to learn from the mistakes that you made, and make sure they don't happen again. Be better because this happened.