The answer is no you cannot run a separate equipment grounding wire whether green insulated or bare. It must be in conduit or sheathed like the other conductors. I'm not sure if your 50 year old wiring is the old knob and tube or just 12/2 with no ground but either way to get a ground wire you are going to have to run new nm-b 12/2wg(with ground) sheathed electrical cable cable.
Your new panel with half new wire in your house would be 12/2wground also which would have a black/hot conductor, a white/neutral/grounded conductor, and a bare or green/equipment grounding conductor. 12/3 is incorrect nomenclature for house wiring but 12/3 w/ground is where you have a black/hot conductor, a red/hot conductor, a white neutral/grounded conductor, and a bare or green/equipment grounding conductor.
The NEC now requires 2 ground rods outside the house 6' apart or more if resistance to ground is above 25 ohms. I don't think it was required a few years ago and even now 4' deep doesn't cut it. The NEC requires a continous bonding wire from the main panel to one rod and then to the other so that all rods and the panel are bonded. Harold must be thinking about separate grounding bars for the neutral and equipment ground in the main panel because you absolutely DO NOT run a separate wire from the neutral grounded bar in the main panel to one ground rod and a separate wire from the equipment grounding bar in the main panel to another ground rod. The whole idea of the main panel is to have the neutral bar and the grounding bar bonded to the main panel. Then only one ground is run out to the ground rods. (qualify that with a few utilities that bond their equipment ground to the ground rods at the meter but then run a separate ground wire in the conduit with the 2 hots and the neutral to the main panel) Remember however that on subpanels the grounding is NOT bonded to the subpanel and a separate wire equipement grounding wire is run to the main panel.
If you have a question about any of this, then absolutely talk to your electrician, electrical inspector, and the utility.
If you want 3 prong outlets at the 2 wire circuits, then you have to use all gfci outlets and put the no equipment ground sticker on them.
Fail to follow code can cause problems like shock, fire, death, loss of value on resale, and having to fix it right when an inspector finds the problem either pursuant to an inspection on the electrical or one done by a home inspector. Good luck.