Parents [topic-は] I [subject-が] that university [to-に] enroll do [nominalizer-こと] [object-を] are-expecting.
~ことを期待する (to expect someone to do X) uses the nominalized clause as the object of 期待する. ている marks the ongoing state of expectation. 入学する (to enroll/enter a school) is the standard verb for university admission.