Catelyn Indicted Tyrion Because Caught Red Handed

When Catelyn arrived at the inn of the crossroads with Ser Rodrik, she was in no way prepared to move forward with her intention to eventually indict Tyrion. What changed her calculus, when he noticed her, is that Catelyn felt guilt at being recognized, since she and Rodrik were in disguise. It's a lot like she lost her temper. There was the panic--fear--then the compensation for it--anger. Catelyn characteristically translates her guilt into accusation by leveraging her anger to overcome her fear. It's a pattern of behavior with her and notable in other characters, too. I've come to call it "turning on the hunter."

Catelyn and Ser Rodrik knew it was a risk to stop at the inn, but after Lord Mallister rode right past them, Catelyn assured Rodrik they would not be recognized because they are so bedraggled by travel. But when they hear Tyrion's man say "my lord of Lannister" both Rodrik and Catelyn panic:

"Oh gods," Ser Rodrik said before Catelyn reached out to silence him, her fingers tightening hard around his forearm.

As Tyrion talks, Catelyn begins to fume in certainty he sent a knife to kill Bran. She's looking straight at Tyrion when Marillion calls to him.

His mismatched eyes started to move away...and found Catelyn. He looked at her for a moment, puzzled. She turned her face away, but too late. The dwarf was smiling "Lady Stark, what an unexpected pleasure," he said.

Catelyn rises to her feet. The description is reminiscent of a dream of being naked in public:

She could hear the muttering and feel the eyes upon her. Catelyn glanced around the room, at the faces of the knights and sworn swords, and took a deep slow breath to slow the frantic beating of her heart. Did she dare take the risk? There was no time to think it through, only the moment and the sound of her voice ringing in her ears.

Catelyn reaches out to her father's bannermen for protection as in self-defense, showing the cuts on the hands. Tyrion describes it as a "plea." Catelyn seems driven by fear for the safety of her loved ones and yet it comes in the form of prosecution, a fury at those who would endanger them.

With Tyrion greeting her warmly, all Catelyn had to do was smile in return, share her table and she'd be able to ask him some questions. She might even have pretended to be going his way and shared the road with him straight to court. But Catelyn was overcome by emotional intensity. Subtly, but importantly, it's the emotional intensity of having been recognized when she thought to pass unnoticed that fills Catelyn with the guilt that causes the panic and fear that triggers the self-defensive anger that provokes Catelyn to indict Tyrion on the spot.