Was re-listening to the Reek chapters from ADWD, and wanted your opinion on the case of Barbary Dustin. Why is she still the Widow of Barrowton? The impression WOIAF gives is childless widows are disposed of immediately when the overlord is competent, so is her being in a position of power a failing of Eddard as an overlord? Or does it imply that there are no other claimants for House Dustin’s seat? Or does she actually have a kid that I missed?

Yeah, she’s an interesting case. I’m guessing it has to do with a few things. 

• 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 House Dustin. 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?