I like the idea Grey Wolf, that could have changed alot, however I dont believe it would have avoided war all together, I think a Great War is bound to happen, maybe sometime in the late 20s early 30s.
Perhaps the Tsar and Tsarina are killed by a radical in St Petersburg while she is pregnant with Alexi. Michael becomes Tsar, he sends the four grand duchesses to be raised by an aunt in Moscow, living in the Kremlin. The girls turn out completely different.
Archduke Ferdinand is spared due to the butterflies but his wife is still murdered. He will remarry a couple years later, this time to a proper European Noble. There is no WWI between 1914-1918.
But can we really get a peaceful century? The Clash of Empires seems difficult to avoid.