My sister Abby, will travel to Mexico, on her vacation.
My sister, Abby, will travel to Mexico on her vacation.
My sister Abby will travel, to Mexico on her vacation.
My sister Abby, will travel to Mexico on her vacation.
The correct answer is the second option, because you don't need a comma before 'on her vacation' or before 'to Mexico', but 'Abby' needs to be separated from the rest of the sentence by commas.