You should obtain a copy of your daughters school attendance record showing that she was in school that day and provide it to the mediator. Since it is unclear why the mediator wanted your daughter there, if the proceeding has been rescheduled, and what power the mediator has in your custody case, I really cannot give you my thoughts on what the court may do. I would obtain the attendance record as soon as possible and provide it to the mediator asking for some type of remedial action. Speak to an experienced attorney in your area who you can give more details to.
Mediation is confidential and no one is sworn in for testimony. Was the mediation court ordered? What County was the mediation in? Without the answers to these questions it is hard to give an answer to your question. If you have proof that your ex lied, I would suggest taking to the next session. If he didn't bring her just to delay the process, that could be very useful to you. You should review the detail of the case with a family law attorney, please feel free to contact my office.
This answer is for informative purposes only and should not be construed as legal advice. This Q&A forum does not create an attorney/client relationship. If you have a legal concern that is important to you, I urge you to consult with an attorney. For those who are concerned about their ability to afford legal assistance, the ACBA's Lawyer Referral Service is here to help: http://www.acbalrs.org .
Typically, the mediator has little authority to enter a court order unless there is an agreement between the parties. Therefore, the fact that he lied to the mediator should have little bearing in your case right now. However, if your county requires the child to attend the mediation session and the father lied about the reasons for her failure to attend, I agree with previous counsel that you should get the attendance record and use it against him at the time of the trial. It may negatively impact his credibility with the Judge.
My response is based solely on the limited information contained in the question. It is not meant to substitute your attorney's advice.
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