Some electrical issues

I am having an issue with my car listed above C55 model. I had the alternator replaced in July of last year so I wanted to run the symptoms by you to see if you might be able to tell me if it's related to that part, or if it's possible I have other issues. ( I don't want to go back to that mechanic unless it's for warranty work)

I was out getting gas last week, and after filling up when I went to turn on the vehicle the key would not turn and I realized the display screen was off and so were all electronics. When I checked battery voltage it was at 12.3v with the engine off. I have a portable jump starter so I decided to use that and it started up fine, with no warning lights at all. I then drove about 20 miles without issue and then a later trip for about 5 miles without issue.
Today when I went to drive my car, I made it a few miles without issue until the car died on me while idling and stopped at an intersection. The car had no electricity and I couldn't turn on hazard lights. I ended up jumping it again and it started fine without any lights on the dash. When I got home I checked idle voltage and it was 13.4-13.7, and 12.4 with the engine off. 
I know the best option is to take the car in and get it scanned for codes, but before I do that I wanted to see if you had any suggestions. The fact that the car needs a jump while the battery is at a decent enough voltage seems to suggest to me that it may be an alternator issue, but I wanted to get your thoughts on where to start.