Correctly powering amplifier and speakers
Supply 12V to both amplifiers, just on one don't turn the volume up as so far, or put a resisitive divider on the amplifier signal input.

You would still need this divider even if you were to use an 11V supply as you'd have to scale the input down to match the lower peak output

if you are connecting the aplifiers to diffrerent sources the divider is not needed, just adjuste the volume control to suit.

These amplifier modules are class D and so are no less efficient operating at reduced volume

to get full loudness it's going to want 50W or so of 12V. So a 3A or more "power brick" is indicated, but music power if often spiky so you may get acceptable performance with a smaller power supply. if you want to used the two amplifiers for different purposes using two powersupplies (one each) may be more convenient.