/lit/ - Literature

Having some trouble, /lit/.
Friend and I are having an argument over something really trivial and I can't get an answer on something this specific by Googling it: whether you ought to place a comma between a single common noun and a proper noun which clarifies it. Example:
>"She held a strong hatred toward her mother, Laura."
versus
"She held a strong hatred toward her mother Laura."
To me, they both feel equally correct, but then I considered the following for plural nouns:
>"He held a strong hatred for his cousins, the Sackville-Bagginses."
which looks at first blush more correct than
>"He held a strong hatred for his cousins the Sackville-Bagginses."
Is it the first option in both cases?