I'm refusing to pay $1300 on a wig for my cousin's wedding after a slight mishap with hair extensions
That's a lot of money. Why do you think they messed up your wig?
I don't think they would have made this kind of mistake with the order. I want what I'm paying for.
$1300 is a lot of money that is owed for services rendered, but now that they have made it to your order, it is your obligation to pay. If you are not satisfied with the wig, you can have them alter it, but you should ultimately pay what you owe.
Not unless I get the right wig. That better be the end. I'm sick of dealing with them.
Just because you didn't like it, that doesn't mean you can't pay. They worked really hard on it, and you owe them for their labor. If you aren't happy with the result, how about you  ask for modifications until you are happy?