It doesn't really seem you can convince Merrill of anything, even her Keeper can't :)

The whole problem with both Anders and Merrill is that while yes, they're useful and are doing mostly good things (until the very end), but they're a fucking blood mage and an abomination. You turn in mages that are far less dangerous or suspicious...

And yes, the existence of ser Alrik (and ser Karras) does make it difficult to believe Meredith knows what she's doing.