This has obviously been discussed many times, but I'm left to wonder...
Had Lenin/Trotsky gotten their wish and brought Nicholas and his family to Moscow for that show trial. Don't you think people as politically savvy as they would realize that A) The Tsar's family could be used as a bargaining chip and this would have made the execution of at least Alexei and OTMA unwise. And B) by executing anyone besides the Tsar and Empress would force a severe backlash...not only by many of those inside of Russia, but the other world powers? Some of whom were related to the Imperial Family.
It's one thing that George V and Kaiser Wilhelm, given their tenuous hold on things in England and Germany respectively, might not have acted while the Tsar and his family were locked in a home in Urals facing an uncertain fate. But once a public trial was announced in a major city such as Moscow, and the possible fate of not only Nicholas & Alexandra but their children was at stake, don't you think certain negotiations would have taken place?
And given that, Lenin, who owed Germany huge for allowing him safe passage back to Russia in the first place would almost certainly have had to comply with demands to exile the children...maybe even spare the life of Empress. Lenin, Trotsky and company took certain measures to distance themselves from the Ekaterinburg murders. They even announced the death of just the Tsar and Alexei (?) first because they feared public backlash as a result of the news of the entire family's execution. Given what we know of their political sensitivity I'd think a show trial followed by a full scale execution of the entire family (on what would have to be ludicrous legal grounds) is something they would not have permitted.