As far as I know, you can go to any store with an automotive section and get a transformer to go from 120vAC to 12vDC. Think about it -- how else could the guys at best buy demo the car audio stuff!
However, it will be a little messy (cables running everywhere), and more trouble than it might be worth.
As for controlling the output from your receiver to the amp, any basic DJ mixer should be able to do the job - they all use RCA plugs as standard for the ins and outs. Plus, you could do some crazy beat matching!
That's the best advice I have.
Brian
ps -- don't you think you'll have more bass than you need? Or is the 'need' outweighed by the 'want'?