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The essential thing about the passive construction is that the subject of the verb (passively) receives the action, instead of (actively) performing it, and thus corresponds to the object of the active verb. In the sentence "Mary took good care of the children", the object of "took" is "good care" ("the children" is part of the adverbial phrase "of the children"): hence, strictly speaking, the passive should be the rather awkward "Good care was taken of the children by Mary".

If we take the words "took care of" together as a sort of compound verb, however, "the children" is transformed into object, allowing it to become subject in the passive: "The children were taken good care of by Mary".

So both sentences are defensible from a purely grammatical point of view, though I would agree that the second sounds more natural.

(Where there is a very close connection between the verbal action and a noun governed by a preposition, as in "Dr Chesterfield <i>paid</i> for <i>the ticket</i>", grammarians often call this noun the <b>prepositional object</b> of the verb.)   

Regards,

Samuel

Sam