Randa Martin always wanted high ceilings. Her partner, Richard Lebehn, longed for a chef’s kitchen like the ones in all the restaurants where he had worked.

The couple started getting closer to building their dream home after they moved in 2009 to the Saint Regis Mohawk Reservation, otherwise known Akwesasne, where Ms. Martin was born and raised.

Mr. Lebehn, originally from Pohnpei, an island in Micronesia, got a job as a chef at the local casino; Ms. Martin found work in a doctor’s office. They had moved from Myrtle Beach, S.C., where they met at a dance at the House of Blues in 2001. Ms. Martin wanted a village to help raise their expanding family.

First they rented apartments on the reservation, but those quarters were getting uncomfortably tight as their four children grew older. “Once you get to that age you need your own space, considering two of the children were 6 feet tall,” said Ms. Martin, 45.

Feeling an urgency to move into something bigger, Ms. Martin and Mr. Lebehn began thinking about finally becoming homeowners.