I am reading the book 'Salazar, A political Biography' by Filipe Ribeiro de Meneses it seems that Dom Duarte Nuno tried to tie himself to the Salazar regime after returning to Portugal (and settling in Canidelo, Vila Nova de Gaia). In 1958 he wrote an angry letter to a newspaper denouncing Humberto Delgado, a politician who openly opposed Salazar. The duke also congratulated Salazar on the Angolan war. In 1966 the duke also refers to 'the Great Salazar'. The duke and his family also attended the opening of the Salazar bridge in Porto in 1966.
It seems that esp. Dom Duarte Nuno's sister Da. Filipa was in touch with the dictator.
Edit: he settled at the Quinta Bela Vista in Canidelo, Vila Nova de Gaia: