Sounds like you need two different relationships between People and Family--one to initially link a record by last name and one to link by serial Id field defined in Family. The first gives you an initial match that you can then review and correct on a case by case basis.
People::LastName = FamilyByName::FamilyName
People::_fkFamilyID = FamilyByID::__pkFamilyID
FamilyByName and FamilyByID would be two different table occurrences (boxes in manage | database | relationships) with the same data source table.