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I will help answer your question. You absolutely do not have to sign the order. If you disagree with the order then don't sign and he will have to schedule a hearing. You and he will be governed under whatever order is currently in effect. If provides for visitation for you he can not deny it without being in contempt of the order. I would tell him and her you are not signing and you want the custody provided for under the current order and if he does not than you will file for contempt.
I recommend sending him a copy of your counseling information saying you should not have been admitted and there is no reason why you should not have visitation at a minimum. I would also recommending bring anyone that has observed you and your daughter together recently that can testify that it is a normal relationship. Lastly, your daughter is 16, not 5, and can self report if anything bad would happen during your custodial time. Sounds like a crook to me. I hope this information is helpful and I wish you luck. Don't be bullied into signing.