"Má velkou rodinu, o niž se dobře stará."

[Renardo11]

People say that relative clauses without a pronoun are always defining. The Czech sentence does not appear to be defining; I think its meaning could equally be expressed by "…and he takes good care of it" (I am not suggesting this as an adequate translation; it does not preserve the structure). So I would prefer "…of which he takes good care."

[VladaFu]

People will say anything. What do reputable grammar handbooks say?

And do note that your suggestion is already accepted.