Before Lord Karstark murdered the Lannister boys, could Robb have gotten ahead of the situation? Karstark was clearly not happy with some of the decisions regarding Jamie Lannister even before Catelyn released him, but after the release, could Robb have offered Catelyn as a bride for Lord Karstark to bind him better to his cause? She was not past her childbearing years, so possible children from that match would be kin to the king. Plus the idea of new sons may have soothed his anger.

I think that dramatically misreads the situation. 

Rickard Karstark has been implacably wrathful ever since the Battle of the Whispering Wood, and his responses in ACOK and ASOS are driven by emotion rather than any consideration of policy. Consider that he was strongly opposed to Robb’s peace terms which only generally encompassed the idea that Jaime might eventually be traded back after Tywin’s good behavior, an extreme outlier among the Northern and Riverlords. 

And even if, in some implausible scenario, Rickard Karstark had gotten his wish and Jaime had been executed rather than set free, I still think the inconsolable grief and rage that drove him would have manuevered him into some violent death – if not on the battlefield than suicide-by-king.