Lee,
All I will suggest is that, aside from specific design characteristics, a 3V motor is rarely going to generate the torque a 12V motor provides. And I imagine car mirrors are fairly heavy and cumbersome things to actuate even with a 12V motor. I may be wrong, I've never tried it, but it seems to me...
So before trying to re-engineer everything, I would dig a little deeper into finding an more suitable replacement. I would definately consult the datasheet for both motors for current, power, and torque specifications. Otherwise, you may find out that 3V motor only stalls after all the work to fit it.