Barbey Dustin says that she contributed as few of her men to the Stark host as possible. Would the Starks not be aware of how many men she can raise, and questioned this disloyalty?

Well, this gets us to the twisty nature of the feudal contract. As bilaterally-negotiated documents, feudal contracts could vary dramatically in terms of what kind of service was negotiated –  how many knight’s fees your land was valued at, how many days’ service you were required to provide, how many men you had to bring, etc. 

What this could often result is that there was a difference between the minimum a lord was required to kick in and the maximum they could actually bring to the table, and how many men actually showed up would depend on politics. If the king is popular and/or powerful, if the war is going well and there’s a good chance of winning loot/land, you bring extra men above your minimum requirement so as to gain royal favor. If the king is unpopular and/or weak, if the war is going badly and the risk/reward on participation is bad, you send as few as you can get away with. 

We see this very early on in the War of Five Kings with Bran VI of AGOT: the lords who show up in full force to Winterfell are looking to gain something in return, whether it’s a military command, or Robb’s hand in marriage, or for him to give them some land or some use-rights, or to side with them in a dispute or what. Barbrey Dustin is making much the same political calculation, but in reverse: what’s the least amount of men she can get away with sending without incurring a felony?

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.