I agree with a lot of what you say, especially the fact that someone could have at least helped Nikolai and Aleksandra's children, and that no one helped the White Army really have a chance at some sort of restoration. However, I think that we need to look at George V's decision to not help his cousins from another angle. Could he have helped? Absolutely. But, what would have happened to him and his wife and children? Britain wasn't exactly feeling warm towards the house of Saxe-Coburg and Gotha (Wettin, I believe being the name that the family used), so if George brought in his Russian cousins, with Alix, who was German by birth, he would have sealed his own family's fate. I'm not saying he did the right thing, but I'm saying that he did what he had to do to save his throne and wife and children. Also, we cannot forget that the Romanovs would have parted from each other. The Nikolai, Aleksandra and their children were a very close-knit unit, and I cannot see anyone going willingly if someone couldn't come.
I think it's a little harsh to want the current British Royal Family to suffer for George V's choices. The present monarch, her children, grandchildren and cousins are not responsible, so they should not be made to suffer. The ones who should are the ones who were in Russia at the time, and stood by and watched the family get slaughtered.