Honey, you have booked and paid for your wedding. I'm guessing she has not.
You have reasons for picking that day, you did, it is arranged.
You have no mutual friends, so this is only about YOUR attendance at HER day.
She seems to have been the one that has made a mistake by booking the same date after you did.
If you can calmly ring her and say,
If the date were not important to me, because of XY and Z, I'd consider moving it.
If I'd not actually confirmed and paid for everything to happen on that date, I'd possibly be able to move it.
BUT
The date IS significant to me, and I HAVE confirmed everything, ages ago, it IS all paid for, if I move it I will lose out.
I can't move it, even if I DID want to.
You could ask her to listen to herself, put herself in someone else's shoes for a second and recognise that you have not done this to spite her.
If she can't be reasoned with, frankly you have to say that this is beyond bridezilla that you are sorry you can't be at her day and that she is unwilling to laugh about it, and arrange a 'do' for both happy couples on the other side..
Tell her that if she really feels this way that there is nothing you can do and tbh she is not the kind of person you would be proud to call a friend. Wish her good luck and hang up.