You make a complete copy of your freshly installed Grand Theft Auto V and rename it"Grand Theft Auto V Online". Now you can mod the original Grand Theft Auto V and when you want to play online, you can rename your "Grand Theft Auto V" to "Grand Theft Auto V Modded" and then rename the "Grand Theft Auto V Online" to "Grand Theft Auto V". Make extra sure that you never add any mods to the version you're going to use online as it will cause you to get banned. When you're finished playing online, make sure to reverse the procedure.
GTAV will only play from it's originally installed directory and rage will only work if it's in the original GTA installed directory, that is why you have to do it like this. You can not launch Rage from a directory that is named differently than the originally installed GTA.