Would putting a second battery in my trunk put more strain on my already struggling 80amp alternator?

a extra battery will add some extra stress to your alternator.but that is not the whole story.a battery that is fully charged is much easier to keep charged than one than one that is even a little low.so, if you are drawing enough amperage that your voltage drops below around 12.6 volts on the bass hits a extra battery would be helpful.