Hi, thank you for your question. Firstly, parental responsibility is not lost by the granting of a child arrangement order and can only be lost if the child is adopted or a court discharges parental responsibility.
Secondly, you cannot "appeal" against the child arrangement order, however depending on whether you agree with your ex-partner or not, you can either apply by a consent order to change the arrangements and the court will approve the order. If there is no agreement by your ex-partner you will need to go through proceedings again. Either way, this must be done using form C100 and a £215 court fee to your local family court.
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A contact or child arrangement order does not result in you losing your parental rights or parental responsibility.
If an order is in place you would need to apply for it to be varied if you have concerns and he would not be able to take her from you outside the arrangements specified in the order.