After that, it is Rands fault for having so little respect for Min that he insists on her riding behind him like some kind of servant. He made an ignorant and idiotic decision, now he has to suck it up and deal with the consequences. Which he does.

I'm sorry, but it's not disrespect to put yourself in a position to best protect someone you love.  Min is not a channeller.  Her knives would be of little use against battle-trained damane.  Min's not a delicate flower, but this wasn't likely to be your typical pubside dustup.  So Rand placed himself where he'd be best able to protect her from Power-based threats: right in front of her.  Of course, he was an idiot for not seizing the source up on the hill, but that's another matter...

If you want to frame this entirely on the basis of 'respect'- Frankly, Min disrespected Rand- she put herself in a situation where, if things got hot, as they were likely to- she'd be depending on the others there to defend her.  The consequences you speak of are something she shares responsibility for.  Is it all her fault?  No.  Was she childish and partially to blame?  Absolutely.  If Rand disrespected her when making a security-based decision, she certainly disrespected him by making herself a liability in spite of his protests.

Edit:

By the way, I like Min.  I just think this scenario was stupid and avoidable.

The link i believe is something wrought of the power, so its a sure bet it'd stop working...

Hmm, do you mean because it's something that deals directly with the Power?

I'm not sure that things wrought with the Power lose their effects inside a Stedding...Power wrought swords and cuendillar probably maintain their properties inside a Stedding...otherwise Darkfriends would have been playing the "let's get all the seals inside a Stedding and break 'em" game for the last 3000 years. ;P

That's a really interesting question.  The only terangreal that I can remember being used in a 'No Channeling Zone'  are the Wells that get used in Far Madding.  But we never see them get used inside of a real, actual Stedding...