Why is Shomron called her bigger sister?
Radak: She is bigger than you. Malchus Shomron contained 10 Shevatim.
Why does it say that Shomron is to her left?
Rashi: Yehudah was in the south of Eretz Yisrael, so the other Shevatim were to her left 1 .
I.e. if one faces east. (PF)
Why does it say that Sedom is to her right hand?
Malbim: The [five] cities of the Kikar were in the south of Eretz Yisrael 1 .
They gathered to fight near Yam ha'Melach (Bereishis 14:3). Presumably, this is near the five cities. Yerushalayim is at the north of Yehudah, for part of it belonged to Binyamin. Yam ha'Melach is not so far south of Yerushalayim. Be'er-Sheva and Eilat are much further south! (PF)