Your language is a little loaded there: arrested vs. abducted, there aren’t attorneys in Westeros, Catelyn wasn’t the one denying him a champion of his choice.
But civil war as the minimum fallout? No.
Yes, Catelyn should have expected political repercussions – the queen had every right to complain to the king about her brother’s treatment and the king had the right to order Ned to give Tyrion up – but she was operating fully within the law and the Lannisters should have responded in kind, especially with their superior political position.
But Tywin making war on a third party is wildly disproportionate to the offense, at a time when the Lannisters had many alternatives.
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