But Catelyn is smart enough that she should be able to weigh the fairly meager cost of the Lannisters in the city knowing she was there against the fairly enormous cost of seizing a son of Tywin Lannister. And Catelyn obviously does understand the repercussions of capturing Tyrion, it's why she flees to the close-by Eyrie instead of far-away Winterfell. Capturing Tyrion is not leverage, it's casus belli- and Cat knows it. And none of this is a reason to hate Cat, Ned's actions lead to a whole lot more deaths in the long run than Cat's do. But I don't think it is fair to say that she was making a shrewd move here, or that she was not at all motivated by revenge. She was doing something dumb, and she was doing it at least in part for revenge.
I agree with some of what you said. But I think a re-reading of the book make change your opinion.
She takes Tyrion to the Eyrie because
1. she hoped to elude the Lannister chase party who would be going towards Winterfell and Riverrun, the 2 most obvious places for her to go.
2. taking Tyrion to the Eyrie would unite her with her sister who sparked the whole conspiracy story with that midnight letter. In the book, it is written that Catelyn believed her sister would have the key information to solving the Lannister Consipracy and ultimately uncovering why there were 2 attempts on Bran's life + the death of the old Hand. She believed that Lysa would be able to effectively question Tyrion and solve the whole mess - yeah, like a Murder She wrote story ala Angela Lanisbury.
3. She doesn't fully realize the warlike implications of kidnapping Tyrion because otherwise she wouldn't have done it. Kidnapping( or killing) Tyrion in open public was the worse possible act she could done. She had no ability to warn her husband and her daughters - not to mention the people of the North or Riverrun of her idiotic actions. But Tywin and the Lannisters would know about the news soon - unless she killed every single witness in that inn.