While Hood's eldest brother Arthur Hood, 2nd Viscount Bridport succeeded their father as Viscount Bridport, the Duchy of Bronté was left to Alexander who became the 5th Duke of Bronté. This was possible because of a special and unusual clause in the letters patent granting the duchy, which allowed the holder to choose as successor whomsoever he wished. The Dukedom of Bronte with its vast estate had been granted in 1799 to Admiral Horatio Nelson by King King Ferdinand III of Sicily, for services rendered in saving his kingdom from French invasion. The Duchy had been inherited by the Hood family by the marriage of Samuel Hood, 2nd Baron Bridport to Lady Charlotte Mary Nelson, suo jure Duchess of Bronte, niece and eventual heiress of Admiral Nelson. In his book The Duchy of Bronte he speaks of his father's great generosity in entrusting him with his Sicilian estate, and his constant reply when asked for advice: "I leave it to you, I know you'll do your best". He first visited Bronte in Autumn 1868, aged 14, with his father, mother and sister Adelaide, only the third time Bronte had been visited by a family member since the creation of the Duchy. He stayed his only night in the Palazzo Ducale, the family's townhouse in the town of Bronte, before moving on, accompanied by a long mule train, to the Castello Nelson, the seat of the duchy. His first impressions were "extremely favourable", and he was sad at the prospect of returning to England at the end of the four week visit. He was formally given the estate by his father in 1870 or 1871, when by right of his ownership he became 5th Duke of Bronte, according to the original letters patent. In 1873 he started his residence at Maniace, for 9 months, having been sent there with Jane Thomson, the governess of his boother and sister, who stayed for 20 years. In 1903 he purchased land in Taormina, Sicily, to build a large villa called "La Falconara", still under construction at the time of the 1908 Messina Earthquake. He erected a large Ionian or Celtic cross, made of local lava, in memory of Admiral Lord Nelson at Maniace, following the complaint of his aunt Jane Sarah Hood when visiting, that no monument existed, to which the Duke replied in jest that his epitaph in St Paul's Cathedral stated "Si monumentum requiris circumspice". It is inscribed on the base Heroi Immortali Nili. In memory of his father in 1905 he erected a 40 foot high obelisk on the highest point of Serraspina, about 5,000 feet above sea level, the base of which he inscribed in Latin as follows:
