Tywin's plan of battle was to have the North overcommit against Tyrion's riders at which point he would flank them, Bolton was more cautious and did not do this, a mistake the Greatjon likely would have leading to the destruction of the army. I don't think giving Roose control of a part of the army had anything to do with the betrayal. Bolton smelled weakness and likely would have changed colors if he had 50 or 5000 men once Robb lost the North and the Karstarks, and the Freys were plotting their treachery.
The parlay didn't work, but that failing is Renly's arrogance and vanity, and Stannis's intransigence; the advise she gives and actions she favors are sound.
Which is the thrust of my defense of Catelyn, the basic argument is she is the reason we cannot have nice things; all the failings of those around her are pinned on her. The Red Wedding is brought about by Robb's actions, Stannis + Renly failing to unite is entirely due to their own failings and the sole reason Lannisters still sit The Iron Throne, she would have prevented the loss of the North by keeping Theon, she would have kept Tyrion hostage if her sister had heeded her advise.
And Catelyn's notion of peace may well have been a good one, Robb had no right to a crown and his own father recognized Stannis's succession. The war he fought brought ruin to the north and was based in a desire for vengeance.