I just did some research on Florida law and it appears that you have the right to appointed counsel in Florida for termination of parental rights cases at all stages. Here is the information. I suggest you ask your private attorney to file a motion with the appellate court to appoint an attorney for you in the appeal under Florida statute 39.013. See the information I have cut and pasted below...
Fla. Stat. Ann. § 39.013
Fla. Stat. Ann. § 39.807
Right to appointed counsel at all stages of proceedings
Right to appointed counsel for termination of parental rights
39.013(1) “All procedures, including petitions, pleadings, subpoenas, summonses, and hearings, in this chapter shall be conducted according to the Florida Rules of Juvenile Procedure unless otherwise provided by law. Parents must be informed by the court of their right to counsel in dependency proceedings at each stage of the dependency proceedings. Parents who are unable to afford counsel must be appointed counsel.
39.013(9)(a) “At each stage of the proceedings under this chapter, the court shall advise the parents of the right to counsel. The court shall appoint counsel for indigent parents. The court shall ascertain whether the right to counsel is understood. When right to counsel is waived, the court shall determine whether the waiver is knowing and intelligent.”
39.807(1)(a) “At each stage of the proceeding under this part [Part XI: Termination of Parental Rights], the court shall advise the parent of the right to have counsel present. The court shall appoint counsel for indigent parents.”