In this case your failure is tied to your charging system not recharging the battery. That is why your battery died in the first place and why the new one is dying. Your alternator is not doing its job, either because it has failed or because the drive belt is slipping and needs to be tightened. On such a new car, neither option seems likely, but I would start with the drivebelt. I think your failure is a matter of happenstance and bad timing, not the dealership's mechanics.
I share your distrust of mechanics and do all my own mechanical work, have for many years now. I also drive very old cars, so they are sure to need repairs after a while, but with yours only being 5 years old I would not expect to have a failure in the charging system like you have, unless there are a lot of miles on the vehicle.
If you have a battery guage in your car instead of an idiot light, you should be able to tell if the alternator is charging. With the engine off, note the voltage (probably around 9 volts with a dead battery that won't start the engine). Then have the car jumped from another car or battery charger and the volt meter will read about 13 volts. Start your car and removed the battery cable from the charger or other car and check your voltage again. If it is back down to 12, 11, or lower then you know your charging system is not working properly. If it is 14 volts or so, then it is normal and I would look at battery cables, the connectors themselves being loose or not clean.