Is it permissible to give one's sister money from a usurious bank account for her to buy wedding clothes, knowing that she lives with the same family?

The profits from usurious banks are ill-gotten wealth from which one must repent and dispose of whatever portion of it is in a Muslim's possession. This is done by giving it to the poor and needy, constructing roads, building mosques, and similar public utilities. If your sister is poor, then there is no harm in helping her; otherwise, it is not permissible.