Jesus Christ. This myth is worse than herpes the way that it keeps popping up.
You vehicle is not "an extension of your home." Never has been. That phrase (or any similar phrase) is totally absent from statutes or cases. in fact, your vehicle is so much NOT AN EXTENSION OF YOUR HOME that there is an entirely different set of laws regarding search and seizure of you home, or your automobile.
THIS.....
The answer to the original question is you can carry in your car because of O.C.G.A. 16-11-126(a)
O.C.G.A. § 16-11-126
Having or carrying handguns, long guns, or other weapons; license requirement; exceptions for homes, motor vehicles, private property, and other locations and conditions
(a) Any person who is not prohibited by law from possessing a handgun or long gun may have or carry on his or her person a weapon or long gun on his or her property or inside his or her home, motor vehicle, or place of business without a valid weapons carry license.
If you are legally able to posses the handgun, then you can carry in those 4 locations, regardless of whether you have a GWCL or not.
"Extension of your home" is not a reason and does not exist in Georgia's firearm carry laws.
Jerry