I think this issue is best addressed by a civil litigator who specializes in governmental immunity cases. You should expand your attorney search criteria.
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Normally governmental employees, which a mediator is, has at minimum qualified immunity, and sometimes absolute immunity.
However, qualified immunity can only be pierced if you can prove that the mediator intentionally, with knowledge of, or constructive knowledge of, violated your constitutional protections. From your post it seems as though she made a recommendation to the court and advocated for certain provisions, but it does not appear, at least from your post, she violated a consitutional protection. Look at 42 U.S.C Section 1983 on how to sue individual governmental employees.
That being said, that does not render you case untenable. If you feel the FCS department was negligent in some way, you may be able to file a suit under the FTCA. However, based upon your post I am doubtful you would be successful.
I understand your frustration, and I hope this assisted you in some way.
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Take a look at Civil Code section 47. The statute will almost surely be used by the mediator as a defense to a defamation cause of action. You further likely waived your expectation of privacy by agreeing to the mediator.
Nonetheless, there are ways around the statute as well as ways around qualified government immunity if you can establish malice. It is a very high legal standard.
In your family case, you can always challenge the mediator's findings. Again, doing so is difficult but not impossible.