Charlotte of Wales is born a boy (named Charles ITTL) and marries a surviving Grand Duchess Maria Alexandrovna, older daughter of Tsar Alexander and Elizabeth Alexeievna. This is a preliminary list of their offspring, not including marriages. I'm thinking that either Elizabeth or Charlotte will be Queen of the Netherlands, while George will marry Sophie of Württemburg. Mary or Sophia might wind up with a son of Louis Philippe.
Charles III, King of the United Kingdom of England, Scotland, and Ireland (Charles Augustus; b. 1796, d. 1864) m. Grand Duchess Maria Alexandrovna Romanova (b. 1799, d. 1869) in 1815, had issue
1) Elizabeth of the United Kingdom (Elizabeth Caroline; b. 1816)
2) Charlotte of the United Kingdom (Charlotte Alexandra Mary; b. 1817)
3) George V, King of the United Kingdom (George Alexander; b. 1819)
4) Mary of the United Kingdom (Mary Augusta Amelia; b. 1821)
5) Alexander of the United Kingdom, Duke of Kent (Alexander Frederick Paul; b. 1823, d. 1832)
6) Sophia of the United Kingdom (Sophia Caroline Matilda; b. 1824)
7) Charles of the United Kingdom, Duke of Kendal (Charles Edward Augustus; b. 1829)
An update that nobody asked for.
Charles III, King of the United Kingdom of England, Scotland, and Ireland (b. 1796, d. ?) m. Grand Duchess Maria Alexandrovna Romanova (b. 1799, d. ?) in 1814, had issue
1) Elizabeth of the United Kingdom, Princess Royal and Grand Duchess of Baden (b. 1816, d. ?) m. Alexander, Grand Duke of Baden (b. 1816, d. ?) [1] in 1835, had issue
1) Karl Friedrich, Grand Duke of Baden (b. 1837, d. ?) m. Luise of Prussia (b. 1838, d. 1923) in 1857, had issue
2) Marie of Baden, Princess of Orange (b. 1839, d. ?) m. William of the Netherlands, Prince of Orange (b. 1836, d. 1882) in 1857, had issue
2) Charlotte of the United Kingdom, Queen of the Netherlands (b. 1817, d. 1878) m. William III, King of the Netherlands (b. 1817, d. 1889) in 1837, had issue
1) William of the Netherlands, Prince of Orange (b. 1836, d. 1882) m. Marie of Baden (b. 1839) in 1857, had issue
2) Marie of the Netherlands (b. 1837, d. 1842)
3) Alexander of the Netherlands (b. 1839, d. 1874)
4) Anna of the Netherlands, Princess of Prussia (b. 1842, d. ?) m. Albert of Prussia (b. 1837, d. 1906) in 1860, had issue
5) Maurice of the Netherlands (b. 1846, d. 1852)
3) George V, King of the United Kingdom of England, Scotland, and Ireland (b. 1818) m. Sophie of Württemburg (b. 1818) in 1839, had issue
1) Charles of the United Kingdom, Duke of Clarence and St Andrews (b. 1842, d. 1859)
2) Mary of the United Kingdom, Princess Royal and Princess of the Netherlands (b. 1844, d. ?) m. Henry of the Netherlands (b. 1820, d. ?) [2] in 1873, had no issue
3) Sophia of the United Kingdom, Queen of Portugal (b. 1846, d. 1919) m. Pedro V, King of Portugal (b. 1837, d. ?) in 1864, had issue
4) William IV, King of the United Kingdom of England, Scotland, and Ireland (b. 1852) m. Marie of Saxe-Altenburg (b. 1855) [3] in 1873, had issue
4) Mary of the United Kingdom, Tsarina Maria Alexeievna (b. 1821) m. Tsar Alexander II of Russia (b. 1818) in 1838, had issue
1) Alexandra Alexandrovna Romanova (b. 1839, d. 1843)
2) Tsar Nicholas II of Russia (b. 1841, d. 1919) m. Alexandra of Denmark (later Alexandra Feodorovna; b. 1842) in 1859, had issue
3) Alexander Alexandrovich Romanov (b. 1843, d. 1896) m. Marie of Hanover (later Maria Georgievna; b. 1849, d. 1904) in 1871, had issue
4) Mikhail Alexandrovich Romanov (b. 1845, d. 1913) m. Marie of Mecklenburg-Schwerin (later Maria Pavlovna; b. 1854, d. ?) in 1872, had issue
5) Alexei Alexandrovich Romanov (b. 1847, d. 1908)
6) Maria Alexandrovna Romanova, Duchess of Saxe-Coburg and Gotha (b. 1849) m. Ernst III, Duke of Saxe-Coburg and Gotha (b. 1841, d. ?) [4] in 1867, had issue
7) Elizabeth Alexandrovna Romanova, Queen of Wurttemberg (b. 1852, d. ?) m. William II, King of Wurttemberg (b. 1848, d. 1921) [5] in 1871, had issue
8) George Alexandrovich Romanov (b. 1856) m. Marie of Waldeck-Pyrmont (later Maria Georgievna; b. 1857, d. 1889) in 1877, had issue
9) Paul Alexandrovich Romanov (b. 1861) m. Alexandra of Greece and Denmark (later Alexandra Georgievna; b. 1870, d. 1892) in 1887, had issue
5) Alexander of the United Kingdom, Duke of Kendal and Stratearn (b. 1823, d. 1832)
6) Sophia of the United Kingdom, Duchess of Penthièvre (b. 1825) m. Charles d’Orléans, Duke of Penthièvre (b. 1820) in 1842, had issue
1) Antoine Philippe d'Orléans, Duke of Penthièvre (b. 1845) m. Antónia of Portugal (b. 1845, d. ?) in 1867, had issue
2) Marie Amélie d'Orléans, Princess of Saxe-Coburg and Gotha (b. 1847) m. Albert of Saxe-Coburg and Gotha (b. 1844, d. ?) [6] in 1866, had issue
3) Sophie Églantine d'Orléans (b. 1848, d. 1849)
4) Louis Alexandre d'Orléans, Prince de Lamballe (b. 1849, d. ?)
7) Charles of the United Kingdom, Duke of Cambridge (b. 1832, d. ?) m. Feodora of Hohenlohe-Langenburg (b. 1834) in 1857, had issue
1) Charles, Duke of Cambridge (b. 1859, d. 1937) m. Marianne of Prussia (b. 1864, d. 1941) [7] in 1883, had issue
2) Victor of Cambridge (b. 1862, d. 1863)
3) Mary of Cambridge (b. 1865, d. 1868)
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[1] Son of Grand Duke Charles and Stéphanie de Beauharnais, IOTL he did as an infant.
[2] The Princess Royal's search for a husband is rather arduous. She had first hoped to marry the widower King Pedro, but he preferred her younger sister. Other suitors included the future King Umberto of Italy and a number of British lords, but King George and Queen Sophie flatly refused to allow both of their daughters to marry Catholics and Mary refused to marry a British subject. She eventually met the widower Prince Henry while visiting her aunt Charlotte and her cousins in the Netherlands and the two married about a year later.
[3] A rather unimpressive wife for a British king but there is a noticeable lack of truly suitable princesses of age with William. Plus, IOTL Marie seems to have been well received by the Prussian court so I figured she would work well enough.
[4] Ernst III is the eldest son of Prince Albert of Saxe-Coburg and Gotha and his TTL wife, Marie of Württemberg (b. 1816). Ernst was previously married to Anna of Hesse and by Rhine, but she died of puerperal fever after giving birth to a stillborn daughter.
[5] This match is, of course, arranged by Queen Olga of Württemberg.
[6] Albert is the younger brother of Ernst. Like his great uncle Ferdinand, he converts to Catholicism after his marriage to a Catholic woman.
[7] Daughter of Anna of the Netherlands and Albert of Prussia.