A couple of years ago my wife had a Jaguar XJS with an aftermarket alarm (already installed when the car was purchased).
One day, the car wouldn't turn over...I thought the battery was due for a replacement, so I dropped a new one in. Everything was okay for about a week and then again, completely dead.
Local mechanic said charging system seemed fine and would do other tests. My wife figured the alarm was the culprit and asked them to yank out the brain...they did.
Never had a starting problem since then.
In your case, if the alarm has a faulty brain, it could be leaving an open circuit, obviously something that draws plenty of juice...I would have them yank the alarm computer out and swap it for another...if the problem persists, it will take diagnostics.
BTW 12.3V is low for your charging system, but not enough to suck your battery dry in a few hours...
2009 ML350 (84K) - Family vehicle
2001 CLK430 Cabriolet (71K) - Wife's car
2005 BMW 645CI (124K) - My daily driver
2012 Mustang V6 (60K) - Daughter's car