This is a great point. You're going to need a serious 12v power supply for the car amp. You're better off using a home theater amp than a car audio amp, which will likely have many more options and features specific to interior home audio. Either way, the amp should be matched with both the power source and the drivers, and the 12v is going to be an issue. Converting power is usually a lossy, inefficient and heat-riddled procedure. Converters to do this can also be costly depending on spec.

I am unsure what model subs you have, but from my experiences, you don't get so much quality reproduction as you do SPL out of a sub enclosure designed for an automotive application. Yes, there are high end subs out there, but your average subwoofers have a tendency to mud up the low end. If your goal is loud, you can probably still pick up a cheap used HT amp or receiver amp to do what you want (craigslist, classifieds, ebay, thrift stores). If you're shooting for quality, though, you may want to reconsider your approach.

If your receiver has a line out or tape out, you can run that (line level) to the input of a small aux power amp that you can use to drive the sub. The volume knob on the master (receiver amp in this case) will also adjust the line volume going to the sub amp, so you can just set your levels on the second amp once and forget it.

As always, OP, you're welcome to post any car audio related questions to /r/CarAV.

Also, I love your UN, MasterBettyFTW.