My car stalls out and quits when I'm coasting or sitting idle, gunning gas brings it back?

My car stalls out and quits when I'm coasting or sitting idle (super scary on the highway). The only way to start the car again is to hold the gas pedal down. I can feel the car starting to act up because the a/c blowers will shut off and my steering wheel will lock up, so I gun the gas, and it comes back. The thing is, I have my little hud display on the battery voltage, so I see when it does that it drops down to 12.10 volts-ish. I just got the battery and alternator replaced to try and fix it, but it's still doing it. I suspect it might be my fuel injection system. Could somebody maybe narrow it down so I know what to ask for at the mechanic? Thanks!