The reason they love Yuri so much goes into the reality of the setting. First, the bandits: outlaws have no reason to spare their victims, especially if they have an "arrangement" like in this case. Witnesses could lead the authorities back to them, so kill the men, and enslave the women for a bit of rape before you get bored and kill them. Even if the merchants get away, most merchants were living paycheck to paycheck - losing their goods would be a one-way ticket to poverty, and there are no welfare systems. Not only that, but the suspicion against strangers means you have no friends in the area to help you, and many to suspect you work with the bandits and should tossed in the gaol for safety's sake.
Now, how about Viscount Winebelly? Well, he has multiple ways to abuse his power. First, as the local lord, he is the law. You need to appeal to his overlord to stop him, and good luck doing that without so much as a shaved penny. By the time you even see his overlord, your daughter has long since been raped and deflowered, and probably has a bastard in her belly, so there's precious little point beyond avenging the wrong. Even if his overlord acts, if Viscount Winebelly is a good vassal, all you can expect is a slap on the wrist for the fat schmuck. Your broke and broken family can now look forward to a future where your daughter has to whore herself for a living.
Not only that, Yuri was quite generous in forgiving Alan shittalking his noble house when most other lords would at minimum smack him in he face. As for offering his daughter to Yuri, that's plain good sense - a young lord from a prestigious family with a fief married to Arsha kicks Alan's family two or three steps up the social ladder; his daughter is now a lady who enjoys some protection from louts like Viscount Winebelly; a secure local base for trade expansion; and explicit patronage that protects Alan from other lords.
As for Arsha, give her a break. Yuri saved her not only from death, but from a life of destitution, disgrace, and despair, twice in one day. She's allowed to fall for the handsome young lord.