^ But didn't Littlefinger want that to happen?? He's the one who told Cat about the dagger, no?

Don't be deceived by him, everything he does or says is for a reason.
Based on what information Cat had the moment, it wasn't stupid... 1) She didn't personally know Tyrion, so she couldn't have possibly known that Tyrion would indeed not be stupid enough to give an assassin his own dagger. 2) The information about the dagger came from an old friend that she trusts. 3) It would've raised enough suspicion had Tyrion returned home telling everyone where he had seen Catelyn on the road. 4) They call Tyrion the "Imp"...

It's not fair to be prejudiced, but that's how people work.
It was Catelyn's chance to immediately do something she thought was right, or return home knowing that the "enemy" once again is ahead having information it wasn't supposed to have. Mehzzles