It's more that a high opinion of Karin as a hero overshadows it.
Louise is currently in the process of assembling Evil forces and striking against Good (if currently a bit corrupted and doing some bad things) country. She uses Evil magic, her eyes glow with Evil pink fire and she has Gnarl as her adviser. Overlords complete with the Gauntlet and the Tower are as Evil as it gets, so striking against them is unquestionably Good if technically blasphemous. So that's what Karin would do, daughter or no. From her perspective, letting Louise roam freely is letting the forces of Evil to take over her homeland, which is not something any respectable hero would allow.
And sure, Louise may try to reveal her "true plan," but, well, you can't trust Evil people. I mean, they object to the speeches of various Popes, for one thing.
I would note that normally it would be a completely reasonable course of action. Louise is rather unique among Evil Overlords for aiming at something else than world domination or absolute power, or other classic goals. I am sure Valliere Duke can cite plenty of examples of various family members going Evil and turning against their parents without it being some kind of secret Good plan. Mostly people corrupted by his family, I would wager.
There is, of course, also always an option of redemption, but it doesn't always work and redeemed big bads tend to die in their last heroic act anyway. Plus, social combat is crap, and with her stats Karin wouldn't be able to win it anyway.