Do I need to fire my daughter's original attorney before hiring a new one to appeal her criminal conviction

Since you are not the attorney's client, the attorney has no duty to inform you or to return your phone calls. If your daughter has already been sentenced, she likely has only a short time after the sentencing to file appeals. Once the deadline passed, she would have a very difficult time just on the procedural grounds. If you want to hire an attorney for your daughter, you should just hire the attorney you want. The attorney will worry about the procedures.

Your daughter can have more than one attorney representing her, and you can ask the new attorney you hire about your concern that your daughter's first attorney failed to adequately keep her informed and has apparently abandoned your daughter as a client. If your new attorney concurs, then she or he will know what steps to take to address the situation. The bottom line is that you do not need to wait for the first lawyer to voluntarily step aside before you retain new counsel.