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From Catelyn's POV, taking Tyrion captive was an awesome thing. From Tyrion's POV, well, you can figure that one out yourself.
At the inn, Catelyn said they were going to Winterfell, but instead she's heading toward the Vale, where her sister is in charge.
This is a problem because (a) Tyrion's father will send people north to find him when he's really going east; and (b) the High Road to the Vale is very dangerous because of the wild animals and wild mountain clansmen.
And of course, the clansmen attack their small group. To save themselves, Catelyn has to give weapons to Tyrion and his two servants. In turn, Tyrion saves Catelyn. So everyone's happy, right? Except for the few people who die, of course.
Tyrion also points out that Petyr is a liar and that Tyrion never bets against his own family, contradicting what Petyr said about that fancy dagger.