You should begin by discussing these concerns with your lawyer, which may ultimately resolve, any reservations about his or her fee.
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"It's a simple family dispute. I won a unanimous jury decision." That does not make it a simple appeal, and even a relatively straightforward appeal is a major project. I would have expected, in any event, that the financial terms of the appeal would have been agreed upon between you and the attorney beforehand. But every state, so far as I know, has some mechanism to address and resolve fee disputes. Find out how such disputes are handled in your state and, unless you and your attorney are able to clear the matter up between yourselves, initiate the necessary procedure.