I think you set a precident when you try to help your child by giving her an escape. It may be too late to give this advice, but could you not have suggested to your daughter that the option of staying in the daycare and standing up to her friend may make her feel better about herself in the long run? Listening to her story and empathasizing with her feelings are important and are things that you did. However I think it is important to try to teach kids how to deal with other kids on their own. You could have advised her to go back to the friend and say, "I was hurt when you told me you didn't want to be my friend anymore but after thinking about it, I've decided that it's better for me to not be friends with someone who says mean and hurtful things and who would throw away a friend she has had for a long time for really no good reason. Of course I'm immature, I'm 11 years old, etc..." You get the idea. I don't think talking with the friend's mother and involving her so quickly was the best idea, either. If your daughter didn't think she could stand up to the friend and keep her dignity, you would be a very nice mother to accomodate your daughter by finding her new daycare. But, it could be your daughter's choice, ask her, "Do you want to stay in this daycare, stand up to this girl and show her that you are strong, honest and thoughtful or do you want to never go back, give that girl the power that she can push other kids around whenever she wants and have me put you in another daycare where the kids could be just as mean?"
Like I said this advice may be too late coming and also, it is just my opinion with very limited information. You know your daughter better than anyone and that you would find her a different daycare over the hurt of losing a best friend makes you a very nice mother that any kid would love to have.