Working with family and leaving the business?

I once worked for a small family owned grocery store. My aunt and uncle received items in the back while filling in at the register when needed. My cousin also worked there as the primary cashier. I stocked shelves and worked the meat counter. It was only the four of us working the entire store.

Once I was trained to work the register though, my cousin started showing up less and less, either showing up late or taking entire days off. He clearly knew he could get away with it since his parents owned the place and pretty soon, his parents started to work harder due to his constant absences. 

Eventually got fed up with their refusal to fire him and secretly started making plans to find a new job. One night after the store closed, I asked to speak to all three of them and officially gave them my two weeks notice. My aunt and uncle seemed unhappy but my cousin was very angry and said 'WHY WAIT TWO WEEKS? IF YOU DON'T WANNA STAY, THEN  LEAVE TOMORROW! GET THE F*CK OUT!" That shocked me since it was his laziness that made me want to leave. I was trying to be professional and give them a proper notice but he seemed to take it personal.

Anyways, been working at my new job for a year now but I always think back to how I left the family business and wonder if I could've handled it better? Was I justified in my leaving? Anyone ever work at a family business before?