Honestly, I don't know why people love to argue over such things.
The Charger broke down because it HAD to break down. Why did it have to break down? IT BROKE DOWN BECAUSE THE STORY NEEDED IT. Period.
They had to leave their flat because the story needed to move forward. The school burnt down because the story needed to move forward. They left the city leaving Syd behind and Mom joined them because the story needed it. Now the Charger broke because it needed to break.
Deal with it.
It isn't realistic. So what. Deal with it: you know what, there are no zombies. You know what, you don't fuck your adopted daughter. You know what, you don't fuck your adopted daughter's best friend while having an affair with your adopted daughter. You know what, you don't fuck mom & daughter at the same time.
So, when the story tells you that your Charger breaks down, well... deal with it.