Well said
The Wales children the future George V and his siblings were far less keen on their Danish holidays than their Romanov cousins
In fact the revolution's biggest impact on George was a slightly critical comment about Alicky (the Empress Alexandra Feodorovna) being very foolish and the reactions of his mother (who he doted on) and his sister Victoria (who was closer to her cousin's).
The overriding aim of the British Government in 1917 was to prop up the Provisional Government hence the initial asylum offer later it was rescinded at the King's insistance due to adverse reaction in Britain and by the time that was done it was clear the Provisional Government couldn't have accepted the offer - they had been required to give guarantees Nicholas would not be allowed to leave to the Bolshevik members of the Duma (to that end Queen Alexandra was asked to stop writing inflammatory letters to her sister for example)
George was acting in the interests of his country and it only seems difficult to those who as you say romanticize Nicholas and Alexandra in light of their and their children's ultimate fate.
1917 was a particularly difficult year for George domestically and the year that saw him abandon his german titles, sign the titles deprivation act and change the family name to Windsor.
Nicholas had been told in his mother's hearing on the last time he saw her just days after his abdication to leave the country and not return to Petersburg - he refused to listen.
The couple were later offered the chance for some of their loyal courtiers to take the imperial children to Finland again the offer was refused.
Nicholas like many of his relatives left it far too late to leave the country.
It just seems to me to be an invented story.
I cannot imagine that in either the strict Russian or British courts that this kind of tom foolery would be tolerated for even a second.
Maybe they were able to get away with it while visiting their grandparents in Denmark, there are lots of stories of royals including Alexander III and Edward VII acting incognito while in Denmark, in a way they never could in their home countries.
I don't find it upsetting George V refused Nicholas II asylum. They obviously shared some facial characteristics and they may have been friends, albeit they actually spent very little time together as adults but they were very different men.
One was a constitutional monarch, the other was an authoritarian dictator.
People sometimes like to forget that when they romanticise the Romanovs.
Had Nicholas spent more time looking to the way George operated as King and the success that George had, he might not have ended up in the situation he did.
Ultimately George placed the survival of his dynasty before everything else. I can respect that. He is arguably the most significant British monarch in centuries.