Question: Who reigned over Duchy of Saxe-Coburg and Gotha from 1844 to his death, and was married to Princess Alexandrine of Badin?

Context articles: Princess Alexandrine of Baden
Friedrich Josias, Prince of Saxe-Coburg and Gotha
Princess Dorothea of Saxe-Coburg and Gotha
Princess Amalie of Saxe-Coburg and Gotha
Gustav Badin
Ernest II, Duke of Saxe-Coburg and Gotha
Princess Mathilde of Saxony (b. 1936)
Princess Clotilde of Saxe-Coburg and Gotha
Andreas, Prince of Saxe-Coburg and Gotha
Alfred, Duke of Saxe-Coburg and Gotha

Princess Alexandrine of Baden (Alexandrine Luise Amalie Friederike Elisabeth Sophie; 6 December 1820 – 20 December 1904) was the Duchess of Saxe-Coburg and Gotha as the wife of Ernest II.
 She was born the eldest child of Leopold, Grand Duke of Baden and his wife Princess Sophie of Sweden.
Friedrich Josias, Prince of Saxe-Coburg and Gotha (Friedrich Josias Carl Eduard Ernst Kyrill Harald; Callenberg Castle, 29 November 1918 – Amstetten, Austria, 23 January 1998) was the head of the Ducal Family of Saxe-Coburg and Gotha and titular Duke of Saxe-Coburg and Gotha from 1954 until his death.
Princess Dorothea Maria Henriette Auguste Louise of Saxe-Coburg and Gotha (30 April 1881 – 21 January 1967) was a princess of Saxe-Coburg and Gotha (German: "Prinzessin von Sachsen-Coburg und Gotha" ) by birth and the duchess of Schleswig-Holstein (German: "Herzogin zu Sachsen" ) through her marriage to Ernst Gunther, duke of Schleswig-Holstein.
 Dorothea was born in Vienna, Austria, the second child and only daughter of Prince Philipp of Saxe-Coburg and Gotha and Princess Louise of Belgium.
Princess Marie Luise Franziska "Amalie" of Saxe-Coburg and Gotha, full German name: "Marie Luise Franziska Amalie, Prinzessin von Sachsen-Coburg und Gotha, Herzogin zu Sachsen" (23 October 1848, Coburg, Saxe-Coburg and Gotha – 6 May 1894, Schloss Biederstein, Schwabing, Munich, Kingdom of Bavaria) was a Princess of Saxe-Coburg and Gotha by birth and a Duchess in Bavaria through her marriage to Duke Maximilian Emanuel in Bavaria.
 Amalie was the fourth child and second eldest daughter of Prince August of Saxe-Coburg and Gotha and his wife Princess Clémentine of Orléans.
 Her youngest brother was Ferdinand I of Bulgaria.
Adolf Ludvig Gustav Fredrik Albert Badin, né "Couchi", known as Badin, (1747 or 1750 – 1822), was a Swedish courtservant and diarist, originally a slave, butler of first Queen Louisa Ulrika of Sweden and then Princess Sophia Albertine of Sweden.
 His original name was Couchi, but he was commonly known as "Badin", which means mischief-maker or trickster.
Ernest II (German: "Ernst August Karl Johann Leopold Alexander Eduard"; 21 June 1818 – 22 August 1893) was the sovereign duke of the Duchy of Saxe-Coburg and Gotha, reigning from 1844 to his death.
 Ernest was born in Coburg as the eldest child of Ernest I, Duke of Saxe-Coburg-Saalfeld, and his duchess, Princess Louise of Saxe-Gotha-Altenburg.
 Fourteen months later, his younger brother Prince Albert was born, who became consort of Queen Victoria of the United Kingdom.
 Ernest's father became Duke of Saxe-Coburg and Gotha in 1826 through an exchange of territories.
Princess Mathilde of Saxony, Duchess of Saxony (German: "Mathilde Maria Josepha Anna Xaveria, Prinzessin von Sachsen, Herzogin zu Sachsen" ; born 17 January 1936 in Bamberg, Bavaria, Germany) is a Princess of Saxony and member of the House of Wettin by birth and a Princess of Saxe-Coburg and Gotha as consort to Prince Johannes Heinrich of Saxe-Coburg and Gotha.
 Mathilde is the fifth and youngest child of Friedrich Christian, Margrave of Meissen and his wife, Princess Elisabeth Helene of Thurn and Taxis, and a younger sister of Maria Emanuel, Margrave of Meissen, the late head of the Royal House of Saxony and senior claimant to the defunct throne of the Kingdom of Saxony.
Princess Marie Adelheid Amalie "Clotilde" of Saxe-Coburg and Gotha, full German name: "Marie Adelheid Amalie Clotilde, Prinzessin von Sachsen-Coburg und Gotha, Herzogin zu Sachsen" (8 July 1846, Neuilly-sur-Seine, Île-de-France, Kingdom of the French – 3 June 1927, Alcsút, Hungary) was a Princess of Saxe-Coburg and Gotha by birth and an Archduchess of Austria through her marriage to Archduke Joseph Karl of Austria.
Andreas, Prince of Saxe-Coburg and Gotha, Duke of Saxony (given names: "Andreas Michael Friedrich Hans Armin Siegfried Hubertus"; born 21 March 1943) has been the head of the House of Saxe-Coburg and Gotha since 1998.
 He is the grandson of Charles Edward, Duke of Saxe-Coburg and Gotha, the last ruling duke.
Alfred (Alfred Ernest Albert; 6 August 184430 July 1900) reigned as Duke of Saxe-Coburg and Gotha from 1893 to 1900.
 He was the second son and fourth child of Queen Victoria of the United Kingdom and Prince Albert of Saxe-Coburg and Gotha.
 He was known as the Duke of Edinburgh from 1866 until he succeeded his paternal uncle Ernest II as the reigning Duke of Saxe-Coburg and Gotha in the German Empire.