OK, here's my try at a constructive answer:
Trotsky gets shot in the head during one of the late battles of the Russian civil war, making him a great hero of the revolution and a non-threatening brain-damaged idiot.
After Lenin dies, to avoid a struggle for power, the near-vegetable is made the figure head leader. Stalin, in this world, is still powerful but feels comfortable enough with the arrangement to follow a more collegial path.
In the late 30s, political instability in Germany leads to a military dictatorship with a rubber-stamp conservative dominated Reichstag. This militarist Germany goes about reclaiming the Rhineland, agitating for anschluss, trying to undermine France, Poland and the Soviet Union, and generally being an annoying revanchist power, but not to the point where Britain is repelled, leading to Germany and Britain working to roll back Versailles together. The British, of course, aren't actually friends of Germany, but to the Soviet Union, it looks like they are facing an Anglo-German capitalist alliance slowly building up to destroy them.
The politburo of the Soviet Union, except for the idiot figure head, is inspecting a new steel mill in 1939, when a freak industrial accident kills them all. The USSR is now in the hands of a brain dead moron, and proceeds to act like it, launching an invasion to destroy the German murderers of their beloved revolutionary leaders.
My less constructive answer:
Trotsky's ideology is heavily misunderstood. 1) Because maligning him was a hobby of the Stalinists, the Democratic Socialists and the anti-Socialists. 2) Because Trotsky himself started advocating very different policies when he was outsted from political power in the USSR.
His ideas on "continuous revolution" actually added up to being more in favour of greater openness to the West and greater trade with the West than Stalin's ideology. It was not an ideological position that committed Trotsky to suicidal wars.
Equally, Stalin's "socialism in one country" did not mean that Stalin was not absolutely committed to spreading the revolution. Rather, Stalin was saying "let's grow strong here so we can support the revolution elsewhere in the world when it does happen".
Furthermore: Trotsky has a snowball's chance in hell of becoming leader of the USSR. Yes, you can trace contorted paths where events all add up just right to putting Trotsky in charge. But honestly, Nick Clegg had as much chance of becoming Prime Minister of the UK. Also, in the incredibly unlikely event of Trotsky gaining power, 1) there's no way in hell Trotsky has as much power as Stalin, he simply does not have the talents required to be a powerful dictator, let alone talents that compare to Stalin's in this field, 2) Trotsky wasn't a suicidal idiot.
Also, don't make the mistake of thinking Hitler was the only potential leader of Germany that wanted to violently overthrow the order in Europe in service to their ideology. German militarism got an unjustified sanitization during the Cold War - if you actually look at the political aims of the militaristic right in interwar Germany, they had just as much potential to be mass-murderers as Hitler's lot. Just their mass-murdering would be more aimed at Poles and Russians, not Jews.
fasquardon