Does this sentence have two meanings or one meaning only?

                       Anne onun kıyafetini dolaptan aldı.

Is it possible that it is the mother´s dress?

Onun=his or her (excluding the mother)

I think it is a typical mistake that English speakers make. And there is a reason also. They do not trust the possessive suffix because they do not have such a thing in their own language. This issue should be given more importance in text books. I often see explanations of the type "it gives you the feeling that o is someone else here". No. It doesn´t give the feeling. It is someone else.

Yes. Thanks, si++.

Just have been pointed here by Abla What about this sentence?

Anne, kendisinin kıyafetini dolaptan aldı.

Would this mean the mother´s dress? Or would it be still someone else´s dress?

Yes, it would be.