When Tsar Nicholas II of Russia, first cousin of George V (their mothers were sisters), was overthrown in the Russian Revolution of 1917, the British government offered asylum to the Tsar and his family. Worsening conditions for the British people, and fears that revolution might come to the British Isles, led George to think that the presence of the Russian royals might seem inappropriate under the circumstances.
Despite the later claims of Lord Mountbatten of Burma that David Lloyd George, the Prime Minister, was opposed to the rescue of the Russian imperial family, the letters of the King’s private secretary, Lord Stamfordham, suggest that it was George V who opposed the rescue against the advice of the government. Advanced planning for a rescue was undertaken by MI1, a branch of the British secret service, but because of the strengthening position of the Bolshevik revolutionaries and wider difficulties with the conduct of the war, the plan was never put into operation.
When, in May,1940, Kaiser Wilhelm II, in exile in Doorn, Holland, and eighty-one years old, was surrounded by the invading German army, which had instructions not to fraternize with him – Hitler wanted to keep a possible rival whom he despised at arms’ length – Churchill asked King George VI for his consent to send an RAF plane to Doorn to bring the Kaiser and his wife to safety in England.
The Kaiser was George V’s first cousin; both were grandchildren of Queen Victoria. George VI agreed. After a night of indecision, the Kaiser decided to reject the offer, on the grounds that he did not want to give Churchill a propaganda victory and that he did not want to leave the Dutch in the lurch in their hour of need. This did not prevent the Kaiser from sending Hitler a telegram of congratulations four weeks later when he entered Paris, an aim that had eluded the Kaiser in WWI.
Eric Koch’s book, The Weimar Triangle, is available at Indigo-Chapters and in your local bookstore. 
It was the House of Saxe-Coburg and Gotha, rulers of a tiny duchy, that started it all. How they managed to marry so well is still a puzzle to us today.
The explanation: the exceptional charm and ambition of Leopold, later King of Belgium and exploiter of the Congo.
When Napoleonic troops occupied the Duchy of Saxe-Coburg in 1806, Leopold went to Paris. Napoleon offered him the position of adjutant, but he refused. Instead, he took up a military career in the Imperial Russian Cavalry. He campaigned against Napoleon and distinguished himself at the Battle of Kulm at the head of his cuirassier division. In 1815, at the age of 25, Leopold reached the rank of lieutenant general in the Imperial Russian Army.
In Carlton House on 2 May 1816, he married Princess Charlotte of Wales, the only legitimate child of the British Prince Regent (later King George IV of the United Kingdom) and therefore heiress to the British throne, and was created a British field-marshal and Knight of the Garter. On 5 November 1817, Princess Charlotte delivered a stillborn son; she herself died the following day.
Clearing the path – after the reign of George IV – for Victoria, his sister’s daughter.
The rescue attempt in 1917 makes sense. King George’s rejection of the idea does not. The Kaiser’s refusal to go to England also makes sense, in view of his being German, after all.
George V seems to have thought the presence of the Tzar’s family would infuriate local Bolsheviks, who might make trouble. (I agree this is hard to understand.) As to the half-English Kaiser, in whose arms his grandmother Queen Victoria allegedly died, he once said he felt truly at home only in England.