Side note: people in this book don't stay settled for long – except for all the poor peasants who never leave the farm where they were born.
The two of them stop at the Old Crossroads Inn while in disguise.
Catelyn wonders whether to go to her dad Hoster Tully's place (not so far) or her sister's place (which is very dangerous to get to), and decides she should go north.
Unfortunately, Tyrion's party, including Yoren, stops at the inn on their way south and Tyrion notices Catelyn (when a silly singer named Marillion calls on Tyrion).
So Catelyn asks all the men there at the inn if they are loyal to her father. Since this inn is close to Tully land, all the men there are sworn to lords who are sworn to her father (so they better say yes).
When they do say yes, Catelyn takes Tyrion captive. Uh oh.