My mother doesn't like us snacking.

Literal

Mother [topic-は] us [subject-が] snack [nominalizer-の] [object-を] does-not-like

間食する = to snack / eat between meals. 私たちが間食するのを好まない — the nominalized clause 'us snacking' is the object of 好む (to like). が marks the subject within the nominalized clause.