I have read something in a biography on Empress Zita about the inheritance dispute; if I recall correctly, in his will Duke Roberto appointed his brother-in-law Infante Alfonso Carlos of Spain (husband of Duchess Maria Antonia's oldest sister) as guardian of his retarded children born from his first marriage to Maria Pia; and as guardians of his children born from his second marriage (who were all minors) he appointed his widow Duchess Maria Antonia and their brother-in-law Duke Karl Theodor in Bavaria (husband of Maria Antonia's sister Maria José). When Duke Karl Theodor died in 1909, Infante Alfonso Carlos became guardian also of Roberto and Maria Antonia's children (but jointly with Maria Antonia).
Prince Elias and Princess Beatrice were Roberto's only children not to need a guardian, because they were both adults and "normal" (and however Beatrice was already married at the time of her father's death).
The aim of these provisions of Roberto's will was to grant all his children the same means.
In his will, Roberto also stated that his eldest son Enrico would become Duke of Parma, but due to his mental issues Prince Elias would act as regent.
The problems were caused by the bad relationship between Duchess Maria Antonia and Prince Elias, and started when Duke Roberto was still alive. After marrying Roberto, Maria Antonia became mother of 12 children and also carefully took care of Roberto's other children. Elias, instead, simply didn't care neither of his siblings and of his half siblings.
Things worsened after Elias' marriage to Archduchess Maria Anna of Austria-Teschen, because of the strong loathing of Maria Anna's mother, Archduchess Isabella, to the Bourbon-Parmas.
When Duke Roberto died in 1907, Elias started to manage the Ducal Family's wealth without caring of his stepmother, siblings, and half-siblings; as he was the acting Head of the Family, he claimed larger and larger shares of his family's asset, and this exacerbated his relationship with Duchess Maria Antonia.
Eventually, after long years of fights, an attempted agreement and some court cases Elias got the better of his stepmother and half-siblings and he was given half of the whole inheritance of Duke Roberto (included Chambord Castle).
Some more informations about some of Roberto's children:
Maria Luisa married in 1893 to Prince Ferdinand of Bulgaria, with whom she had four children; one of them was King Boris III (husband of Princess Giovanna of Savoy).
Enrico and Giuseppe were indeed mentally retarded, but strangely the one was an expert of numismatics and the other knew all the names, model and serial number of all the locomotives of the Austro-Hungarian railways.
Beatrice married in 1906 to Count Pietro Lucchesi Palli, with whom she had four children; she and her family later took care of her sisters Maria Teresa and Luisa in her estate in Brunnsee.
Elias married in 1903 to Archduchess Maria Anna of Austria-Teschen, and they had one son, Roberto (who succeeded his father as Duke in 1959 till his own death in 1974), and seven daughters; only one married, Alice, in 1936 to Infante Alfonso of Spain, Duke of Calabria (she still alive, aged 94).
Adelaide, Francesca and Antonia all became nuns at St. Cecile convent in Solesmes.
Sixte married in 1919 to Hedwige de la Rochefoucauld, daughter of the Duke of Doudeauville; they had a daughter, Princess Isabelle. Sixte died in 1934.
Xavier became Duke of Parma in 1974, at his half-nephew Roberto II's death; he married to Countess Madeleine of Bourbon-Busset, and was the father of Duke Carlos Hugo
René married in 1921 to Princess Margaretha of Denmark, and they were the parents of Prince Michel (husband of Princess Maria Pia of Savoy) and of Queen Anne of Romania; they had two more sons.
Luigi married in 1939 to Princess Maria Francesca of Savoy, the younger sister of Giovanna, the wife of Luigi's half-nephew Boris III of Bulgaria; previously in the early 1930s an attempt to arrange a marriage between Maria Francesca to Luigi's nephew, Archduke Otto of Austria (son of his sister Zita) was made by Empress Zita, but it failed. Louis and Maria had four children together.
Henriette was the only of Roberto and Maria Antonia's children to have health issues, as she became deaf and mute after a fall when she was a child; however, she quietly spent her life in Italy, where she died in 1987.
Gaetano, the last child, was married from 1931 to 1955 to Princess Margarete von Thurn und Taxis, with whom he had a daughter, Princess Diane. He died in 1958 in a car crash.