Introduction to the Lannister Family Dynamics

In the complex web of the Westerosi aristocracy, Tywin Lannister stands as a figure of unmatched cunning and ambition. His marriage to Joanna Lannister was purported to unite House Lannister with a powerful noble family, ensuring security and prosperity. Yet, beneath this fa?ade of alliance lies a deeply personal betrayal that would test even the most stoic of Minds.

Discovering the Truth: Tywin's Anger and Betrayal

Should Tywin Lannister find out that Jaime, his twin, is not his biological son, the ramifications would be catastrophic both emotionally and politically. Upon the revelation, Tywin's first reaction would undoubtedly be one of profound and crushing fury. This discovery would invert the very fabric of his trust, blinding him to the infidelity of his wife, Cersei Lannister. The pain of being deceived would be compounded by the realization that his trusted siblings and his legacy are all fraudulent.

Tywin's anger would be exponentially intensified by this newfound knowledge. He would question not only Cersei’s integrity but his own judgment and the credibility of his house. The loyalty of those closest to him would be called into serious doubt, making Tywin’s world crumble beneath him. The emotional turmoil would extend to his harshest critic: himself.

The Political Climate: Removing Trouble Pawns

In the realm of politics, Tywin Lannister operates with a cold pragmatism. If he indeed discovers that Jaime is not his son, Tywin would view Cersei and Jaime as merely pawn-like entities - assets to be managed but now, more trouble than they are worth. Cersei, the Dowager Queen, and Jaime, the Kingsguard, would both be under scrutiny.

Implications for Inheritance Rights

Jaime's role as a Kingsguard prevents him from claiming any significant inheritance now. Cersei, however, no longer holds any claim to the Lannister inheritance. Tywin could use this opportunity to assert his dominance and remove his "troublesome" pawns quietly. Disinheriting them would come with greater ease in this political climate. However, Tywin would tread carefully, believing that any public announcement might stir unrest and embarrass the family further.

Tywin's Inner Turmoil and the Disinheriting Process

Although Tywin despises his only legitimate son, Tyrion, for his dwarf status and the tragic death of his mother, Joanna, the revelation about Jaime might offer a glimmer of hope. Tywin's inner thoughts and motivations remain firing in the background, where he mulls over possibilities of remarrying to produce another heir. However, this speculates his unease and grief.

Regardless of his inner musings, Tywin Lannister would be driven by his need to secure the honor and pride of House Lannister. If he were to disinherit Jaime and Cersei, he would do so discreetly and provide a plausible explanation. If anything, he would go to extreme lengths to protect the prestige of his house. His fear of mockery and disrespect from other houses would keep him from airing this shameful secret in the open.

Conclusion: Tywin's Euclidean Anger and Strategic Beginnings

Considering the psychological and political impact on Tywin Lannister, the discovery that his twin Jaime is not his son would be a turning point. His response would be a complex amalgamation of anger, betrayal, and a renewed strategic effort to secure House Lannister's honor. This revelation would force Tywin to reassess his priorities and reassume the mantle of the Lannister patriarch with his characteristic ruthlessness and cunning.