You say that she should just fight the court order. However, the order was made by the Family Court system, not the civil court system. Family Courts operate in secrecy and it virtually impossible to appeal their decisions. Moreover, defendants are liable for contempt of court if they talk to journalists about their case, or attempt to publicise what went on in court.
Indeed, the poor lady in this case is currently being threatened with prison for publishing a video on the web highlighting her plight. If she ends up in prison for this, she won't be alone - more than 200 people were locked up in 2005 for contempt of the UK's family courts. See http://www.timesonline.co.uk/tol/comment/columnists/camilla_... for further information.