Does appointment of an attorney for the children over a fit father's objection violate his right to parental-relations?

QUESTIONS PRESENTED The trial judge in Petitioner’s divorce and custody dispute appointed an attorney for the children (AFC) over Petitioner’s objections and despite the unequivocal fact that his children were not abused or neglected. The AFC actively litigated against Father’s interests and the expressed wishes of his children, to continue their relationship with their father. Father was compelled to subsidize a portion of the AF'C’s legal fees and expenses under threat of imprisonment. The intermediate appellate court denied Father’s appeal and his motion to supplement the record on appeal. Father appealed to the New York Court of Appeals (NYCA) and also argued that the intermediate court violated his due process rights by ignoring unequivocal facts and all of Father’s legal arguments. The NYCA denied the appeal for lack of finality and denied his motion to reconsider, despite ongoing irreparable harm to Father’s rights to free speech and parental relations. 1. DOES APPOINTMENT OF AN ATTORNEY FOR THE CHILDREN OVER A FIT FATHER’S OBJECTION VIOLATE HIS RIGHT TO PARENTAL RELATIONS? 2. DOES COMPELLED SUBSIDIZATION OF A COURT APPOINTED ATTORNEY FOR THE CHILDREN VIOLATE A FIT FATHER’S RIGHT TO FREE SPEECH? 3. DOES COMPELLED COOPERATION WITH A COURT APPOINTED ATTORNEY FOR ii THE CHILDREN VIOLATE A_ FIT FATHER’S RIGHT TO FREE SPEECH? 4. DOES A COURT APPOINTED ATTORNEY FOR THE CHILDREN RAISE THE RELATIVE VOICE OF A_ PARTY OPPONENT BY LITIGATING AGAINST THE INTERESTS OF A FIT FATHER AND FOR THE INTERESTS OF HIS ESTRANGED WIFE IN A CUSTODY DISPUTE? 5. DOES COMPELLED SUBSIDIZATION OF A COURT APPOINTED ATTORNEY FOR THE CHILDREN VIOLATE THE TAKINGS CLAUSE? 6. MAY THIS COURT REVIEW AN ORDER OF THE HIGHEST COURT OF NEW YORK STATE WHEN THERE ARE FURTHER PROCEEDINGS YET TO OCCUR, BUT ALL NEW YORK STATE COURTS ENFORCE WRITTEN POLICIES, CUSTOMS AND PRACTICES THAT VIOLATE RIGHTS PROTECTED BY THE FEDERAL CONSTITUTION AND A LITIGANT AND HIS CHILDREN WILL SUFFER IRREPARABLE HARM IF CERTIORARI IS NOT GRANTED?