How did Franz Joseph’s marriage to Elisabeth affect his family life?

Franz Joseph’s marriage to Elisabeth in 1854 was characterized as a "stormy" union, despite his deep and lasting attachment to her. Their family life was marked by significant tension and tragedy:1

• Court Conflict: Shortly after the marriage, Elisabeth became estranged from the imperial court due to frequent conflicts with her mother-in-law, Archduchess Sophia, and her own impatience with the rigid etiquette of the Viennese aristocracy.2
• Parental Strain: The couple had four children: Sophie, Gisela, Rudolf, and Marie Valerie. The relationship between Franz Joseph and his only son, Rudolf, was strained by political differences; the Emperor’s conservative views stifled Rudolf’s liberal reformist ideas, leading to the son's political isolation.34
• Tragedy: The family suffered a devastating blow in 1889 when Crown Prince Rudolf died by suicide in a pact at Mayerling, a shock from which Elisabeth never fully recovered. Elisabeth herself was later assassinated in 1898.243