Can the court appoint an attorney to represent my child in a California family law case?

Yes. Pursuant to Ca family code section 3150. (a) If the court determines that it would be in the best interest of the minor child, the court may appoint private counsel to represent the interests of the child in a custody or visitation proceeding, provided that the court and counsel comply with the requirements set forth in Rules 5.240, 5.241, and 5.242 of the California Rules of Court.