Perhaps you need to tell her you don't like this woman so you don't have to miss out on other trips with your friend. You could say something like "I'd love to have gone to the theatre with you, but I don't know if you've noticed that X and I don't actually like each other too much and I was upset about having to spend an evening with her."
She might be upset that you don't like her friend, but at least will understand (hopefully) that you tried to get along with her, but couldn't make it work.