I'm sure upon inspection you'll be able to tell if the clasp was indeed faulty or if it was broken in another manner. I offer polishing, tightening, repairs to my customers when necessary. I handle enough components to be able to tell if something was "faulty" or put together poorly by me or if it's a case of the wearer not being careful with their item. (Like the woman who purchased a piece for her husband which he wore while working out. He caught the clasp on his shorts, pulled it, and stretched the whole thing apart so it needed to be replaced. That's not "faulty." That's his fault.)
Really...you're talking about a few bucks, so it depends how firmly you want to stick to your policies. Sometimes it's difficult when you feel like you are being taken advantage of to not want to dig your heels in. Especially if you feel like you're being treated rudely. It's not really the same as making a return to a big box store. The cashier at the big box store didn't put her time and energy into making an item to sell. She takes the return and moves on to the next thing. It doesn't come out of her pocket or ruin her day, know what I mean? I think you are probably feeling a little taken advantage of and attacked which makes it harder to want to work with someone. For me personally, a lot of it depends on how the customer contacts me. I've picked up 100% of the costs that weren't even my mistake for customers who weren't rude or condescending just because I felt so badly for them.
Her second message chapped your hide but at the end of the day, it's probably best not to bicker over a couple of bucks and just get her out of your hair.