I don't agree all WOT politics are so bad (too much of the subtleties are only implied, however) but I agree about Elayne and Cairhien. Brandon really sucks at writing politics, and it's fairly clear Jordan had left many gaps there for him to fill.

You're wrong though. Elayne herself has absolutely no claim to House Damodred. She is a Trakand. By her father, she had a bood claim to the Throne is the Houses supported her, but not claim at all to any Cairhienin house.

Then the Seat isn't vacant. Caraline is High Seat. This is a blood nobillity, not modern offices. Caraline doesn't lose her position as High Seat because she's out of the country, no more than Elayne stopped being Morgase's heir when she was out of Andor.

One place where Brandon was simplistic and forgot stuff is that Elayne had secured the support of the very important House Damodred. Caraline has told Rand House Damodred would support Elayne's claim. Secondly, she had the support of another extremely powerful House, Dobraine's. Cadsuane's Aes Sedai should have easily gained her the support of the third powerful House (Riatin), as they had leverage on the High Seat.

Jordan had already did all the political background work in Caihien so that Elayne's claim there would be met largely unopposed and she's gain the throne fast (Dobraine had worked towards that, notably). Brandon overlooked all of the backstory and exchanged it with random simplistic last minute political alliances, incl. with Houses we never even had heard about....

As for Elayne's lands in Cairhien, they've been mentionned before. The three children have inherited extensive holdings from their father. Moiraine has extensive ones, that gives an idea how much her elder Taringail owned.