easiest solution is to request yr wife to sit at front seat:)
yes, ofcourse, matching rear speakers from the company would be best choice.
dont not rotate volume to very high and feed distorted sound to speakers, speakers coils get damaged by small amplifiers.
select an amplifier which fullfills yr need of listening volume.that should be sufficent and easier on yr pocket.
if you have front and rear line-out from HU, 4 channel amp would work fine.