My mother is the type who takes good care of the plants.
Literal
Mother [topic-は] plants [possessive-の] care [object-を] well do person is
植木の世話をよくする人だ = 'is a person who often/well tends to plants.' The relative clause よくする modifies 人, and だ identifies the mother as that type. 植木 (うえき) = potted plants / garden plants.