She cared nought for a silly little sword. But the rest was simply a ridiculous notion. She did not need the barbarians to acknowledge her son as the rightful ruler. And if Tommen acknowledged House Stark's independence, what would stop the other kingdoms from asking for the same? If Harrold Arryn declared himself king, House Lannister didn't have nearly enough men to take the Bloody Gate and conquer the Vale or storm the desert paths of the Red Mountains to attack Dorne. The North was nearly half of the territory of the Seven Kingdoms.