"My ancestors went to the United States."
Translation:Chuaigh mo shinsir go dtí na Stáit Aontaithe.
Imigh is more "go away"/"left" - you wouldn't usually use imigh go dtí.
Sinsearach is a variant of sinsear, and Duolingo isn't testing you on your prior knowledge of Irish, it's teaching you it's own vocabulary. If you report it, the course contributors may add Chuaigh mo shinsearaigh go dtí na Stáit Aontaithe as an alternative solution.