prepositions - Is “her” a possessive or an objective pronoun in “A mother takes care of her children”?

I had a sort of debate with my teacher to whether the her in the sentence

A mother takes care of her children.

is a possessive or an objective pronoun.

I told my teacher that it was a possessive pronoun, as the mother had ownership of her children, but she told me it was an objective pronoun as it had preceded a preposition, making it an object of the preposition.

Which one should be correct, or, should both be considered?