Yes. Members of the media started going after Jackie Kennedy, including suggesting affairs, when that was her husband''s balliwick, Then John died a martyr's death and they backed off. It turned out later that those machinations were created by Rose Kennedy who suspected a coming divorce, which turned out to be true. A month prior to Jack's assassination, Jackie had engaged a well known divorce attorney from Texas where the clan had no influence, presenting him with a dossier about Marilyn Monroe and another with other liaisons discovered and documented by a PI Jackie had hired. Her goal, keeping custody of her children.
Toward the end of WWII and even after FDR's death, certain members of the media went after Eleanor Roosevelt, citing her as a lesbian communist. She responded by killing them with kindness. Whatever her personal choices, she was a great woman who loved her country. But some never forgave her for pushing integration of the armed forces.
Louisa Catherine Johnson Adams, wife of John Quincy Adams, our 6th president was accused by the media supporting his opposition, accused her of being a Tory and a spy. She was also an immigrant.
Andy Jackson's wife is a story in and of herself, as are the many duels he fought over her honor while serving the nation.
First ladies are not voted into office, they are in place, regardless of their own desires, to support their husbands, and therefore not fair game. However our press believes everyone is a fair target because as the self appointed 4th estate the people have a right to know, including whatever lies the 4th estate holds as true. They claim the public has the right to know, and I call BS. Nothing is written in the Constitution or any other laws giving the people the right to know. WWII releases of information proved that true. People were given false data to confuse the enemy. No one who was patriotic complained.
The people may want to know, there is no right to know. The same with First Ladies. The people may want to know, especially the prurient, but there is no right to know her favorite underwear or choice of toilet paper.