Apologies if you've answered this before but in ASOS, why does Tywin propose that Jaime marry Margaery and therefore want to take Margaery out of the running as queen? Should we chalk it up to not wanting to share power with the Tyrells or any other family until he absolutely has to (when Tommen is of age and needs heirs)? What brides would Tywin be happy with for Tommen and Jaime with, hypothetically?
While I’m sure that Tywin wants to retain as much power as possible for himself and for House Lannister, I think it’s a little more nuanced than what you’re suggesting.
Lord Tywin rose as well. “A duty to House Lannister. You are the heir to Casterly Rock. That is where you should be. Tommen should accompany you, as your ward and squire. The Rock is where he’ll learn to be a Lannister, and I want him away from his mother. I mean to find a new husband for Cersei. Oberyn Martell perhaps, once I convince Lord Tyrell that the match does not threaten Highgarden. And it is past time you were wed. The Tyrells are now insisting that Margaery be wed to Tommen, but if I were to offer you instead—”
All of the marriages that Tywin has proposed have been attempts to bring together a fractured realm while strengthening the Lannister hold on the Iron Throne. Tywin was trying to hold the North through Tyrion’s marriage to Sansa. For Cersei, Tywin proposed matches to the Arbor, the Iron Islands, Dorne, and Highgarden:
“I have considered the Redwyne twins, Theon Greyjoy, Quentyn Martell, and a number of others. But our alliance with Highgarden was the sword that broke Stannis. It should be tempered and made stronger. Ser Loras has taken the white and Ser Garlan is wed to one of the Fossoways, but there remains the eldest son, the boy they scheme to wed to Sansa Stark.”
The Lannisters need to bolster their military strength through marriage alliances. At full strength, the Westerlands can field about 35k men, while the Reach can put over 100k men in the field. The Lannisters are far below full strength right now. Also, the Lannister fleet that is anchored off Lannisport has only 20 to 30 ships, and coastal Westerlands lords have only 1-3 warships each. The Westerlands have never been a great naval power, unlike the Redwynes (who have 200 warships) and the Greyjoys, who are currently in rebellion. Some sort of marriage with Highgarden is necessary to secure that military strength, that “sword that broke Stannis”.