"Dear Whack-a-Doodle customer,
It is unfortunate that my cake did not meet your expectations. As per our invoice, I am unable to provide you with a refund. I consider this matter closed."
She's not going to meet with you because she either doesn't still have the cake or she knows she can't prove it was stored properly. Send this last email and then don't respond to her anymore. If her friend contacts you tell her you can only deal with (the original customer) since the contract was with her. End of story.
Agree with this. If she refuses to meet with you, you are under zero obligation to give her anything. We dont walk into stores and demand a refund without returning something, so this is no different.
Also agree with Cathy when she says do not respond to her anymore. There's no point.