Must I shave customers' beards in my father's shop despite my refusal to do so, and is the money earned from this work considered unlawful?

It is not permissible to open a shop for shaving beards, because obedience to parents is not obligatory in disobedience to the Creator, and because earning a livelihood must be in accordance with the Sharia. One can suffice with cutting and shortening hair and trimming mustaches without interfering with people's beards. A Muslim should not hesitate to abandon what violates the Sharia, seeking Allah's help and relying on Him, for Allah has promised the righteous provision and a way out.