Hmm... no i don't think you should pay her for what you could save with the discount! Maybe she misunderstood the whole discount thingy, and might think that the discount is for her half of the order only.
Speak to her, and ask her to explain to you what she thinks.
It's definatly not worth losing a good friend over!!
Good luck, she's been your friend for a long time, cherish her
