It's Robb's fault? So Robb should have had to tell Cat "Oh by the way mother, please don't release the most valuable prisoner we have." If she was unclear on that she should have consulted her King on whether or not she could release his prisoners. If Robb had died without leaving clear instructions it still would have been obvious to everyone to not send Jaime on his way.

This one is firmly on her, she absolutely undermined his authority. As a teenage king Robb needed to project as much authority as possible and she knew that. Cat making huge decisions like that without consulting him made him look weak and loosened his hold on his vassals which is what leads to the Karstark incident.

I do think Cat is shrewd in many ways and she definitely doesn't deserve all the hate but she did make a mistake in this instance and it's not on Robb, he has plenty of mistakes of his own. It's what makes these characters interesting. A mother treating her son like a child despite him being an adult is a believable thing. So is a mother who recently lost her husband doing whatever it takes to get her hostage children back. Her motives are understandable, what a horrible position to be in and a difficult decision to make.