Why is Barbrey Dustin the Lady of Barrowton when she was born a Ryswell and the title came with her husband? He must have had an heir, even if they didn’t have children? A cousin mabye, or someone with a claim? Just like before Jon Arryn had a child, there were some possible heirs. And if his marriage to Lysa would have been childless, Lysa would not be the Lady of the Vale, Harry the heir would have become Lord of the Vale, right?

To quote myself:

First, there probably aren’t any Dustins. She and Willam never had any children, and there’s no mention of brothers or cousins or nephews or the like. So I’m guessing there’s no close claim to Barrowton. 

Second, Lady Dustin’s kin are powerful. The Ryswells have a lot of horses, which means they have a lot of heavy cavalry compared to other houses. And the Rills are a pretty large territory. There are also a lot of Ryswells, relatively speaking, as Lord Ryswell has three sons and a number of nephews besides. Chances are, one of those Ryswell sons is Lady Dustin’s heir, so challenging Lady Dustin means you challenge Lord Ryswell too.

Third, never discount personality. Lady Dustin is hard as nails, she’s been ruling Barrowton for a long time, and she’s got the support of her own people and the vassal houses of Houses Dustin and Ryswell. So dislodging her is going to mean a fight.

My guess is, Lord Eddard preferred to keep the status quo. If Lady Dustin is a good ruler, and a Ryswell is going to inherit, why alienate two powerful families on behalf of some claimant who doesn’t have what it takes to take Barrowton from her?

Also, given the proximity of the Rills to the Barrowlands, and my own theory that Barrowton is a large livestock market and the Rills are a major center of horse-breeding, I think there are very long-standing relationship between the Ryswells and the Dustins indeed.

So it may well be that the Ryswells are the closest kin to the Dustins.