Like her mother when she was young, she liked going to parties.
Literal
She [topic-は] mother's young time [with-と] same [manner-ように], party [to-に] going [subject-が] liked.
と同じように ('in the same way as') is a comparison structure. 若い頃 ('when young') uses 頃 to mark an approximate period. The sentence draws a generational parallel.