The point about this is that there are lots of legal precedents that the judge should not sit in judgment on this case and hence it could be challenged on appeal. How does one do that when one knows neither the name of the mother of her solicitors.
For me the particularly interesting aspect of the secret imprisonment of 11th October is that it appears that the judge imprisoned the mother because the judge did not believe what she said. Now that means that the judge is actually prosecuting the mother for perjury as well as sitting in judgment. The mother said her children were somewhere, but they were not.