Your dad and you went to the store.
Here's why:
* Subject-verb agreement: The subject of the sentence is "your dad and you," which is plural. The verb "went" agrees with the plural subject.
* Preposition: The word "to" is a preposition, and it should be followed by a noun or pronoun (in this case, "the store").
You could also write:
You and your dad went to the store.