Rudolf's daughter Elisabeth called "Erzsi" was brought up by her mother and grandfather Emperor Franz Josef who whoreshipped her.
Her relationship with her mother became very distant when she married in 1900 Count Elemer Lonyay. Erzsi didn't consider it a proper marriage and felt that her mother betrayed her father. In 1902 she married Prince Otto zu Windisch-Graetz, who was also not suitable for an Archduchess. He was originally engagement to another woman, but Erzsi didn't give up and in the Franz Josef had to command Otto to marry his
Four children were born from this marriage: Franz Josef (1904-1981), his wife Ghislaine d'Arschot Schoonhoven wrote a biograhpy about her mother in law (Kaiseradler und Rote Nelken), Ernst Weriand (1905-1952), Rudolf (1907-1939) he died in a motorcar accident and Stephanie *1909 who was most likely the daughter of the Marine Officer Egon Lerch who in action in the Frist World War.
Erzsi was very jealous of other woman and once even shot on one with her pistol, to avoid a scandal the woman was given money.
Like her grandmother the Empress Erzsi liked to travel and Franz Josef did the same as with his wife and gave her money to build/ buy some palace in Austria. Erzsi bought Schloss Schönau which had originally belonged to her uncle Archduke Otto.
In 1924 Erszi and Otto divorced and she met the Austrian Socialist Leopold Petznek. She became a fighter for the Socialists and their cause and was known as the "Red Archduchess". Originally the court granted Erzsi the two elder sons, while the younger son and daughter should live with Otto. But when he came to her home to take the children, Erzsi had invited new friends from the Socialists and told Otto that she would shot herself and the children if he didn't move. Well he did.
Her mother Stephanie wrote her memoirs (I shoudl've been Empress-Memoirs of the last Crownprincess of Austria-Hungary), but Erzsi forbade them to be published, as she felt it a betrayal for her father.
While young Erzsi whoreshipped her children, but was a very unfriendly mother when they became older. Rudoulf was taken out of school and put in a factory. Like when other people he lost all money during the depressions, but Erzsi didn't give him or her other children one cent.
In 1948 Erzsi married Leopold Petznek, who had survived the concentration camp in Dachau. Leopold Petznek died in 1956 and Erzsi in 1963. Her children only got the legal portion while the rest went to the Austrian Government.
There's a book about Erzsi by Friedrich Weissensteiner: Die Rote Erzherzogin, but I think it's only available in German