My questions is where you stopped at a light or stop sign when this happened or were you moving? If you and the old lady were stopped and the third car hit her and pushed her into you then I believe that the 3rd car is the one to be responsible for the accident.
If everyone was moving when it happened then that would probably change things.
Either way, I would write the bike off as a loss and make the other drivers insurance pay to replace it.
Getting rear ended with my bike on my tailgate hatch rack is always one of my biggest fears.

