Question

Do you say my mom and dad's store or my mom's and dad's store

Answer 1

My mom and dad's store

Explanation: If you try to use both of those in a sentence, you'll realize that my mom's and dad's store doesn't make any sense.

Answer 2

my mom and dad's store . If the two nouns own the possessed item together only add 's after the second owner. example ( I went to visit my friends Mary and Joe's house) the house is owned by both of them .
If the two nouns own two separate instance of the same possessed item and add's after both owners. example ( I was always jealous of my sister's and brother's bikes) there are two bikes one owned by the brother and one owned by the sister