Yes, I believe that two yagi antennas connected back to back can be made to work.
Try googling for "passive repeater".
If the antennas are separated by a large distance, you will need very good coax cable to make the connection between them, otherwise the losses in the cable will completely negate the gain of the yagi antennas.
You will not need to screen the antennas from each other, there will not be any oscillation if they "see" each other. (Unless you put an amplifier between them).
An amplifier is not a good idea, it would need to have gain in both directions at the same time which is a bit of an impossibility.
Idea, is there a "car adaptor" which can be used with your phone?
My phone has provision for an external antenna when used in a car.
OK so your car is all bent and battered, but a car adapter/antenna could be a solution to your problem.
JimB