With Lannisters in KL/CR it doesn't matter. It's not like they'd be able to take over Winterfell when Stark's bannermen and own soldiers wer still in the North.
But I guess going to her batshit insane sister's, via an area known to have a bunch of barbaric tribes/thieves, is much better right?
For one, if news spread of Cat taking Tyrion while they were still on the road, and especially news that they were heading to Winterfell, the Lannister's would send out men to look for them on the road to Wintefell, where of course they wouldn't find them. It was merely a plan to throw them on the wrong trail.
Second, Cat thought she was going to a confidant, her sister who had sent her a letter warning her of the Lannisters, blaming them for her husband's death. Someone who she could trust and be safe with. She had no idea how messed up her sister had gotten. It had been years (decades?) since they'd seen each other.
Third, the Vale is essentially impenetrable.
There should be no confusion about why Cat brought Tyrion to the Vale instead of Winterfell, only confusion about why she arrested/kidnapped Tyrion with so little real evidence in the first place.