Ok so, I doubt George and Victoria would have the same, active sex life she and Albert had. He just doesn't fit into her ideal, romantic partner like the way Albert did. However, with a partner less concerned with "taming" her, Victoria would probably fall more into Georgian ways, even if it's just being slightly more active and sociable. Albert kinda turned her into the closest thing he could to a German housewife, George would most likely just have left well enough alone.
In regards to their children, I would say that they'd have maybe 6/7, not the 9 she had OTL, which only stopped because Albert didn't want to have sex anymore. That would probably mean 2 things:
- Victoria is overall a much happier woman, because she isn't constantly pregnant.
- Her weight issues are slightly less pronounced and thus her health might actually fail slightly later than OTL.
So, here's my idea:
Victoria, Queen of the United Kingdom (b.1819: d.1903) m. George, Duke of Cambridge (b.1819: d.1904) (a)
1a) George V of the United Kingdom (b.1837: d.1907) m. Alexandra of Oldenburg (b.1838: d.1900) (a)
1a) Princess Mary of Wales (b.1857)
2a) George VI of the United Kingdom (b.1860)
3a) Princess Theresa of Wales (b.1864)
4a) Princess Beatrice of Wales (b.1870)
2a) William Adolphus, Duke of York and Albany (b.1840: d.1844) - haemophiliac
3a) Princess Charlotte of the United Kingdom (b.1842: d.1919) m. Frederick III, German Emperor (b.1831: d.1888) (a)
1a) Frederick IV, German Emperor (b.1862)
2a) Leopold of Prussia (b.1864: d.1867) - haemophiliac
3a) Princess Augusta of Prussia (b.1866)
4a) Princess Helena of the United Kingdom (b.1845: d.1899) m. Louis IV, Grand Duke of Hesse (b.1837: d.1892) (a)
1a) Alice of Hesse (b.1863)
2a) Margaret of Hesse (b.1866)
3a) Louise of Hesse (b.1867)
4a) Victoria of Hesse (b.1869)
5a) Louis V, Grand Duke of Hesse (b.1873)
5a) Edward, Duke of York and Albany (b.1847: d.1917) m. Princess Pauline of Waldeck and Pyrmont (b.1855: d.1925) (a)
1a) Princess Jane of York (b.1878)
2a) Princess Victoria of York (b.1883)
6a) Princess Louise of the United Kingdom (b.1850: d.1938) m. George I of Greece (b.1845: d.1913) (a)
1a) Constantine of Greece (b.1865: d.1867) - haemophiliac
2a) Alexandra of Greece (b.1867)
3a) George II of Greece (b.1870)
4a) Maria of Greece (b.1872)
5a) Victoria of Greece (b.1875)
6a) Nicholas of Greece (b.1877)
7a) Arthur Augustus, Duke of Cambridge (b.1855: d.1879) - haemophiliac