When I see a sentence like this I translate it in my head as "I don't have y'all's bottles" but I'm sure DL will mark that wrong, lol. Given that English lost the singular vs plural distinction in the second person, I think "y'all" is a fine way to bring it back, but I'm sure I'm in the minority.
In this case a translation for "I do not have your bottles." would be "Io non ho le sue bottiglie" that could work both for the courtesy form AND for "his" or "her bottles".
Pretty messy, I know, but we treat possessive in a different way, they agree to the noun, not to the subject, for third person. You'll probably discover something more in the near future, if you will have any questions, please ask.
Lets tell you a joke> Do you have my bottles young man?
1.Sorry sir,I don't have your bottles,cause I have broke them all :D :D :D
2.I don't have your bottles.I have his/her bottles..XD
Take a closer look at the second joke,cause DL teaches us this type of sentences :-)
Am I right?
In Italian, the possessive is formed from the definite article and the personal pronoun of the possessor, both of which have to agree in gender and number to the thing being possessed.
In English, the possessive is formed from a single possessive pronoun that has to agree in gender (3rd person singular only) and number to the possessor.
In French, the possessive is formed from a single word based on the personal pronoun of the possessor which agrees with the gender and number of the thing possessed.
These illustrate how different languages do the same things differently.