I have an existing wire run from my main panel on the house to a detached garage with three wires: Red, Black and White. No ground. I want to install a new subpanel in the garage. I'll be installing grounding rod(s) for the subpanel.
Grounding rods at the sub-panel are not a substitute for a proper ground to the main panel. The earth is generally pretty high resistance and so will not guarantee that a hot-to-ground short will trip a breaker. Thus, such a short will raise the local ground to near 120 volts.
Bonding hot to neutral (the old 3-wire method) avoids this problem but adds a different problem: if the neutral wire back to the main panel fails, the local neutral/ground can rise to 120 volts through a turned-on 120 volt load. This is why it was banned.
To do it properly and to current code, you need a separate ground back to the main panel. Are your current wires running through conduit? If so, it should be pretty easy to add a ground wire. In fact, if you have metal conduit which is properly installed, you should be able to use it as ground.
