Isn't Tyrion infertile? Is there any significant movement in the Westerlands to supplant the Imp and replace him with Kevan Lannister?
Kevan is currently considered Tyrion's heir, with his eldest twin Martyn the likely next Lord of Casterly Rock given Lancel's status as a Black Brother. There are people unhappy with the dwarf being in charge, but nobody ballsy enough to challenge the Demon of Oldstones, particularly when Kevan seems exhausted and interested in little more than advising his nephew and enjoying the quiet company of his family.
As for Tyrion's fertility, no comment. Droman made him sterile in ADOTN but that's a different continuity. There's a fan theory which suggests Lanna in Braavos (the daughter of the Sailor's Wife) is his and another which says the same about Penny and her brother. Neither are true in this case, but it is possible that Tyrion's whores use moon tea afterward or dump their bastards on the steps of a Sept like so many unwanted children.
Tyrion here hasn't made any moves to seek a wife yet, in part because he's still getting into the swing of things and consolidating his power, in part because he's now a chooser not a beggar, and in part because he isn't sure he wants to force some young girl to marry a malformed man who betrayed his brother and father. He'd likely accept your word on who his heir is in the mean time.
[] The Westerlands will see to themselves. Broken as they are you have no need of guaranteeing their loyalty.
[] Tyrion's likely successor is his cousin Martyn, a boy close to Sansa's age. Betrothing him to Arya would bind the West more strongly to your House.
[] As King you have the power to legitimize whoever you please. Tommen is a sweet boy whatever his parentage and a betrothal to Arya would provide you with a malleable and easily led heir of the West.
[] Tommen is not the only surviving child of Jaime and Cersei, however. Wed Myrcella to Bran and see your eldest brother named Heir to the West.
[] Tyrion's heir is his own to choose or make, but a betrothal between your Houses could strengthen your reign. Perhaps Ser Kevan's daughter Janei to your brother Bran?
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