Discussing other clients a massive breech of confidentiality and boundaries, you just don't do it. Utterly disgraceful on her part, because it was hardly a "slip of the tongue" or accident., and what if you spoke about you to other clients?
Considering the client's proposition isn't particularly an issue, because exploring fantasy can be helpful in the process... and she took it to supervision.
I think you need to find someone new, sorry.
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"It is a joy to be hidden but a disaster not to be found." D.W. Winnicott
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