2014 Malibu Eco/Battery problems

My 2014 Malibu will completely shut off at red
lights, stop signs, etc. and I actually have to restart
the engine (i.e. put the car in park, turn the key,
etc). I understand how the eco system works but I
know the car shouldn't just die. Brought it to my
dealership and was told my engine battery was
leaking and had to be replaced but was then told I
have to replace the trunk battery as well because
the engine battery was draining it. This doesn't
make sense to me. I can see how the battery
would cause the shutdown problem but don't the
two work independently? I thought the trunk
battery only handled certain system when the car
is in eco mode. I don't have any electrical problems
at all when the car is running normal. I'm really
confused and feel like the dealership is pulling a
fast one. Any help would be greatly appreciated.