ASOIAF: Was Tywin invading the Riverlands in Game of Thrones justified by the fact that Catelyn had Tyrion? Or was it an overreaction?

I'd say it was an overreaction but I have to admit, the initial plan was clever.

The original plan was not a full-scale invasion. Because that would have undoubtedly been seen as breaking the King's Peace, and brought down the wrath of Robert Baratheon, the greatest general of the age, down on him.

What Tywin did is send a raiding party headed by Ser Gregor Clegane to commit atrocity. Gregor Clegane and his men wore unmarked men so they (and Tywin)  have some plausible deniability in committing the crimes they were committing. (Of course, the fact that it was Clegane was obvious: there are just not that many eight foot tall knights specializing in atrocities in Westeros.)

The reason he did this to lure the ever-honorable Hand of the King, Ned STark out of King's Landing.  He knew Ned, with his northern philosophy of 'The man who passes the sentence should swing the sword" would come after him. 

At that point his plan was to capture Ned Stark at all costs; after which, he figured that Catelyn would willingly trade Tyrion back for Ned Stark.

But his plan was unwittingly foiled by Jaime, who attacked Ned and broke his leg, rendering him incapable of riding out to battle.

And then everything kind of snowballed.

But yes, I still think that what Tywin did was an atrocity. It was illegal. It was a typical overreaction by Tywin. And it didn't achieve his goals. In fact, it ultimately led, one event to the next to his ignoble death and the probable fall of his house.

Written Apr 25th