I am rewatching season 4 now. Tobias Menzies who plays Frank Randall (and Black Jack Randall) really impresses me as a great actor. In a flashback where Brianna meets Frank at his office, Frank has found an old news article describing the deaths of Claire and Jamie in America. This article tells him that Claire will go back to the 18th century again to be with Jamie. Frank is drinking. He knows that Claire loves Jamie, and that she has not really loved him since she returned. Brianna knows something is wrong and asks Frank, her dad, what is bothering him. Frank listens to Brianna and you can see him considering her questions to him, mulling over the answers to them which he knows he cannot tell her. She would not believe him, and he doesn't want her to know that he isn't her biological father or anything about that story.
That scene is powerful. Tobias says very little in words. Watch the expressions on his face as he hears Brianna's pleading questions, as he wrestles with his desire to talk to her while knowing he can tell her nothing. His expressions during that scene represent some great acting. Watch his face as he hears her question and considers it in its depths before he answers. We the audience know what he must be thinking, and his expressions speak volumes. He is truly a gifted actor.

As for Brianna, I am just sick of her. She has no range of emotional reactions. She is exasperated, or angry, or outraged, or hurt. For the most part, that is her. Time after time she is upset, feels injured, betrayed, outraged, etc. This is a real drama queen.

"You didn't tell me?!" she says as she recoils in anger/horror at the betrayal by her new husband when she learns that he failed to tell her of a newspaper article reporting a 200 year old death. Then she learns that her husband spoke to Fiona about the article. Same thing. "Fiona?! You talked to Fiona about this? About MY mother." Again with the drama, the sense of betrayal, over every detail. Fiona was the one who told him about the article. But that makes no difference, this is yet another detail to feel betrayed about.

In anger she tells him to leave her, to sail away to Scotland and return to the future. And of course later on she cries to her mother that Roger, her husband, left her!

She is a one trick pony. She is angry, outraged, feels betrayed, abandoned, let down, etc. , over and over again. You quickly suffer "sympathy fatigue" and finally just quit caring what she says, how she feels, or what happens to her.