I think she's losing it as things are getting out of control.
The actually pressing issue here is Duke Violet is bringing this matter officially to the King.
Her political faction can't help much, they're likely in wait-and-see mode. Evan being the one who ordered the arrest also means his political faction will be backing this move.
Serena told her to talk with the King instead, but that is also likely not an option. Evan's mother wouldn't let go this wonderful chance to remove the threat to her son's claim for the throne.
The only chance is to have Duke Violet pull his charges and settle this "peacefully" outside the court.
But having a negotiation between adults, with the Violets having the upper hand, will end with lots of compensation and political debts.
So she try intimidating Serena first, thinking she's just a girl, easier to control than adult. She never expect the little girl will not bend and instead provoke her enough to hurt her pride and make her lose better judgment.
As for the Violets, I'm with the impression that many elitist nobles (even in Evan's faction) only see them for their ducal title and money. But they look down on the family for not having the "proper attitude" as a blue-blood. Even in Einrich and Rosemary's engagement, the public image would be closer to the Violets coming under the Heinz's faction.
Evan approaching Serena makes it looks like the Violets are playing both sides though. Opportunist, but at least they are not lowering themselves.
Serena is going to win this intrigue by doing absolutely nothing.
Once Mrs. Heinz make this problem between families, it's no longer Serena's problem. And her father is better suited for this kind of conflict anyway, because now it involves mobilising their family's resources.