Obviously, as a manager you could not discuss one employee with another, so you did the right thing by telling your friend that you would not discuss another member of staff with her.
I can understand you are hurt, but honestly, by giving this woman a job you placed yourself and her in a potentially difficult situation - she is now both your friend and a member of your staff. This is a difficult situation and one that you would IMO have done well to avoid.
I cannot see that you reasonably can object to two members of your staff discussing the difficulties the one was having with you, her manager, nor object to your friend helping this other woman draft a letter of complaint to you.
You and your friend will just need to agree to differ with regards to this third person. Presumably, you were justified in going the lengths of a disciplinary action, and I am sure you know very well that very few employees would swallow that without either justifying themselves or writing a formal complaint about the action you had instigated.
I think you really need to put on your professional hat here, and I am sorry if this is not what you wanted to hear.
I personally would never employ family or friends as it is hard to keep ones professional and private life apart if you do so.