Jake and Melanie supposed to be cousins?

No. They’re Ex husband and wife (sort of)

No. When Mel's fiancee showed up and was at the wrong house thinking it was Mel's house, Bobby Ray opened the door and said he was her cousin to make it appear it was her family's house. Jake who had showed up at the same time and walked up with the fiancee then said he is another cousin. So just after at the civil war reenactment, Jake said he was her ex-husband to which fiancee said "you married your cousin"?