Apparently Dom Duarte doesn´t recognise marriages done by the Portuguese state but only those that are done in church, hence he supports the claim of Diana instead of that of Duchess Rosalinda de Cadaval.
Diana is the eldest daughter of the late Duke of Cadaval with his second wife Claudine Fritz, although Rosalinda (married to Hubert Guerrand-Hermès, the heir of the House Hermès) is actually the eldest daughter of D. Jaime, but born from his first marriage (which was not religious, but a civil wedding).
There was a dispute on the succession to the title, since it was Diana (born from the Catholic marriage) and not Rosalinda (born from the first marriage) to inherit the title. At the time, the Duke of Bragança had to decide on who would inherit the Duchy of Cadaval (since Portugal no longer has noble titles, they're not a matter decided in courts and all things related to it are decided by an entity named Conselho da Nobreza, which has its highest figure in the Duke of Bragança). The final decision was based on D. Jaime's wish, since he made it clear he wanted Diana to inherit the title.
I'm not sure about the details of the agreement that was reached between the parts, but, from what I read in the press, the Duke of Bragança considered a kind of "salomonic" sentence, dividing the various titles of D. Jaime (Duke of Cadaval, Marquis of Ferreira, Count of Tentúgal) among his 4 children.
Diana Mariana Vitória Álvares Pereira de Melo is the 11th Duchess of Cadaval. She was born in Genève, in 1978, as the first daughter of D. Jaime Álvares Pereira de Melo (the 10th Duke of Cadaval) with his second wife, Claudine Marguerite Marianne Tritz. She belongs to the second most traditional family in Portugal (which is a colateral branch of the Dukes of Bragança).
Here's the family's estate:
Palácio Duques de Cadaval
that's why Dom Duarte made his decision so fast.
