Why do you not want the child to testify? If it is merely because you fear the testimony won't be favorable to you, that's not going to get the child excluded from testifying, and you can't simply make up reasons to try to get the court to order that the child may not testify. If the child wishes to testify the court will inquire as to whether testifying is in the best interests of the child. If the court decides against allowing the child to testify in court, then it must provide some other means for the child to express her feelings about the move. As a result, so long as the child is competent to testify (and in general a 13 year-old will be) and wants to express her views, the court will provide some way for the child to do just that. You are not likely going to completely prevent the child from expressing her feelings on it if she wants to have her say. The relevant statute is section 3042 of the California Family code:
(a) If a child is of sufficient age and capacity to reason so as to form an intelligent preference as to custody or visitation, the court shall consider, and give due weight to, the wishes of the child in making an order granting or modifying custody or visitation.
(b) In addition to the requirements of subdivision (b) of Section 765 of the Evidence Code, the court shall control the examination of a child witness so as to protect the best interests of the child.
(c) If the child is 14 years of age or older and wishes to address the court regarding custody or visitation, the child shall be permitted to do so, unless the court determines that doing so is not in the child’s best interests. In that case, the court shall state its reasons for that finding on the record.
(d) Nothing in this section shall be interpreted to prevent a child who is less than 14 years of age from addressing the court regarding custody or visitation, if the court determines that is appropriate pursuant to the child’s best interests.
(e) If the court precludes the calling of any child as a witness, the court shall provide alternative means of obtaining input from the child and other information regarding the child’s preferences.
(f) To assist the court in determining whether the child wishes to express his or her preference or to provide other input regarding custody or visitation to the court, a minor’s counsel, an evaluator, an investigator, or a mediator who provides recommendations to the judge pursuant to Section 3183 shall indicate to the judge that the child wishes to address the court, or the judge may make that inquiry in the absence of that request. A party or a party’s attorney may also indicate to the judge that the child wishes to address the court or judge.
(g) Nothing in this section shall be construed to require the child to express to the court his or her preference or to provide other input regarding custody or visitation.
(h) The Judicial Council shall, no later than January 1, 2012, promulgate a rule of court establishing procedures for the examination of a child witness, and include guidelines on methods other than direct testimony for obtaining information or other input from the child regarding custody or visitation.
(i) The changes made to subdivisions (a) to (g), inclusive, by the act adding this subdivision shall become operative on January 1, 2012.