Let's see, my Mom's mother was from Scotland and her father was from Da Bronx. They all lived in Brooklyn for many years, then moved to New Jersey when Mom was a teen. Mom's accent is pretty much mild Jersey. Her mother had only a light Scots lilt, having come to US at the age of 9, and her father sounded like Archie Bunker. Dad's parents were native NJ, but born in the late 19th century, so they spoke quite properly, without the NYC-influenced Jersey slang and accent. Holiday dinners featured quite an array of accents. Especially if Mom's Scottish grandfather was present - he never lost an ounce of his unintelligible Scots accent.
My sister and her children, all born in NJ, moved to South Carolina when the kids were very young. as they grew, one stayed in SC, two moved to Florida. The Florida kids have barely any southern accent. The SC kid, now 44, sounds like those guys that raped Ned Beatty in Deliverance

. My sister, who lived in NJ to the age of 40, has absorbed about 50% southern twang. Locals can tell she's a Yankee, Yankees think she's a southerner.
So, ya know, no reason to think three people from one family will all sound the same.
