My father didn't allow her to go to the movies alone.

Literal

Father [topic-は] her [subject-が] alone [by-で] movies [to-に] go [nominalizer-のを] permitted-not.

許す (to permit) takes のを — the nominalized clause 一人で映画に行くの becomes the object of 許す. The negative 許さなかった denies permission.