The Dutch and Swedish families are related through their descent from the Waldeck Pyrmont sisters, the duchess of Albany and the Queen Mother of the Netherlands (Wilhelmina's mother).
Yes, I tried to visualize it for myself:
George Victor (14 January 1831 – 12 May 1893) was the 3rd sovereign Prince of the German state of Waldeck and Pyrmont. George Victor was first married on 26 September 1853 to Princess Helena of Nassau, daughter of William, Duke of Nassau. They had seven children:
1. Princess Sophie (27 July 1854 – 5 August 1869); died of tuberculosis at fifteen.
2. Princess Pauline (19 October 1855 – 3 July 1925) married Alexis, Prince of Bentheim and Steinfurt. Pauline and Alexis had eight children
3. Princess Marie (23 May 1857 – 30 April 1882) who married Prince Wilhelm, later King Wilhelm II of Württemberg. They had three children
4. Princess Emma (2 August 1858 – 20 March 1934) who married King Willem III of the Netherlands. The present Dutch royal family descends from this marriage. Her only child was the later Queen Wilhelmina --> Queen Juliana --> Queen Beatrix --> King Willem- Alexander
5. Princess Helena (17 February 1861 – 1 September 1922) who married British Prince Leopold, Duke of Albany. She had 2 children:
5.1. Alice, who married her second cousin once-removed, Prince Alexander of Teck, the brother of Princess Mary, the Princess of Wales (later Queen Mary, consort of George V). They had 3 children
5.2. Charles Edward, last reigning Duke of Saxe-Coburg and Gotha, who married Princess Victoria Adelaide of Schleswig-Holstein She was the eldest daughter of Friedrich Ferdinand, Duke of Schleswig-Holstein, and Princess Karoline Mathilde of Schleswig-Holstein-Sonderburg-Augustenburg. They had 5 children, including Sibylla, the mother of Carl XVI Gustaf of Sweden.
6. Prince Friedrich (20 January 1865 – 26 May 1946), last reigning prince of Waldeck and Pyrmont, married Princess Bathildis of Schaumburg-Lippe. They had three sons and one daughter. Their eldest son was Josias, Hereditary Prince of Waldeck and Pyrmont (German: Josias Georg Wilhelm Adolf Erbprinz zu Waldeck und Pyrmont) (13 May 1896 – 30 November 1967) who was the heir apparent to the throne of the Principality of Waldeck and Pyrmont and a general in the SS. From 1946 until his death, he was the head of the Princely House of Waldeck and Pyrmont. After World War II, he was sentenced to life in prison at the Buchenwald Trial (later commuted to 20 years) for his part in the "common plan" to violate the Laws and Usages of War in connection with prisoners of war held at Buchenwald concentration camp, but was released after serving about three years in prison
7. Princess Elisabeth (6 September 1873 – 23 November 1961) married Alexander, Prince of Erbach-Schönberg. They had four children. As great-aunt of the bride, she was a guest at the 1937 wedding of Juliana of the Netherlands with Prince Bernhard of Lippe-Biesterfeld