Due to the Scandinavian setting of Frozen, the Southern Isles are most likely located somewhere in southern Norway, or possibly Sweden or Denmark, the latter of which is comprised mostly of islands. Because Hans is named after the Danish author Hans Christian Andersen, there is a possibility that he's from a place representing Denmark. Also, since Arendelle is implied to be in Norway, Denmark would logically be the Southern Isles as Denmark is south of Norway in real life. This is further suggested in Frozen Fever, where, after Elsa accidentally sneezes into the horn and causes a huge snowball to be launched, it is shown travelling all the way to the Southern Isles, which is shown to be roughly where Denmark is.
The King and Queen of the Southern Isles have 13 sons, with Hans being the youngest of them. The King and Queen most likely expressed favoritism towards the oldest sons. This left Hans feeling overshadowed, which eventually drove him to emotionally manipulate Anna in order to take over Arendelle. This would be the ultimate declaration of power and strength to Hans. He, as king, would no longer be overshadowed by his brothers.