Once you turn age 18, your parents legally have no control over you any more. As long as you remain on probation, you would be subject to the same terms of probation as when a under age 18, but the PO could not require you to continue to reside with and continue to follow the rules of your parents. If you change residences though, you would need to make sure the proper procedures re: notification of your PO are followed so you don't possibly get a revocation for failure to report, etc.. Good luck.
When you are on probation, you are subject to the terms of your sentence, which includes that if you move from one residence to another that you get permission from your probation officer. Moreover, if the juvenile court judge required you to reside with your parents for the duration of your sentence, then you will have to live there until your sentence ends or until you get the juvenile court judge to remove that condition.
While I am a licensed attorney in the State of Georgia, I am not your attorney, even though I have answered your question here on Avvo. I take the time to answer questions here on Avvo as a public service, and a way to help educate the public about certain aspects of the criminal justice system here in Georgia. If you are in need of more detailed answers or representation, you will have to contact me, set up an appointment, and after a consultation, retain me for my services.