The fact that you are trying to teach both girls a responsibility lesson is great. But remember, you only have control over teaching your own daughter, not the other child. It sounds like you have already taken the time to talk with your daughter about what her friend did and why that wasn't appropriate. Good job!
It's understandable that you wouldn't want the girl back in your house but you feel stuck because your daughter is really missing the friendship. Talk with your daughter about what important friendship qualities are and let her make the decision if she feels this friend is a good friend or not. Then if she makes the decision to continue her friendship, teach her how to be assertive with her friend if a situation like that should arise again. Talk about things they can do to rebuild trust in their friendship and how setting boundaries might be appropriate until the trust is back.
