Hello Tyler.If your 19,and already in a career that you really enjoy,then you've a headstart over most people that age.That's definately a bonus for you.
If I could play Devil's Advocate for a second though,I'd try and keep as open a mind as possible regarding the tensions with the older workers.You mentioned you know your right,but I bet they feel the same way.
It would be similiar to you having a 10 year old boss,and both of you "knew" you were right about something,but you had to do it his way because "He" was the boss.Imagine how that would make you feel,having to take orders from a 10 year old kid?
Regardless,the boss is THE boss,so if that's you,then they'll have to do it your way,since your responsible for the outcome.But being a good boss(or leader) is going to require tactfullness and consideration when dealing with situations like that too!!
I use to have a saying that I loved to say to my boss years ago:"If your the "Boss",and I'm "Nothing",then doesn't that make you the boss of nothing?"
We,re ALL learning everyday.
Good Luck!!