Does the validity of prayer and the acceptance of worship become affected by ongoing family discord with a sister, especially if the reason for it is her pursuit of freedom and committing acts considered unlawful in the brother's view?

Boycotting someone who commits a sin is permissible. If you believe that boycotting your sister will benefit her and deter her from her error, then continue to do so, even if the period is long. If it is not beneficial, then stop boycotting her and try to win her heart through other means. Your boycotting of your sister does not make you one of those whose sins are unforgivable or one of those who sever ties of kinship, as long as its reason is legitimate. This is because the hadiths prohibiting boycotting and estrangement pertain to worldly matters, not religious ones. We ask Allah to accept your deeds and forgive you.