hmmm, alternative history is always a good starting place for writing, but it is always best to first make sure you have a firm grasp of your version of history even if only a small fraction of it will be shown to the player.

In regards, to your history itself I would suggest setting it a little farther into the future. Maybe the early 50's at the height of a cold war between America and Germany.

If you have the Germans delaying their assault on Russia and instead diverting most of their resources to Britain then it is conceivable that they could have conquered Britain and Ireland. If that had happened then the US would have been forced the US and Canada to cease hostilities against Germany due to the fact that they would have lacked the logistical capabilities to launch an offensive across the Atlantic.

In terms of game play story ask yourself this; what is the story I want to tell? Remember that Germany is in the far weaker position when it comes to this invasion. They are far from their supply lines and power base. Fighting in their opponents home territory which is heavily industrialized and the combined area of the us and Canada most likely equals that of the entire German empire at this point. This is not a battle the Germans can win unless you give them an edge.

What that edge is, is up to you and should factor heavily into your story line. Your best bet also is to be more specific with the aims of operation Mjolnir. Invade Canada and US is overly broad and doesn't have any clear aims or objectives. Instead try and figure the over all objective of and purpose of these three simultaneous strikes and how they combine to further the overall German agenda of conquering the US and Canada.

Just some food for thought

What I'm probably going to do is take the arcade approach -- simplify the story for the game, and portray the entire thing in actions rather than words. I can post every detail later. This is a 2d project, not an epic FPS spanning three continents and three years of fighting.

Nice idea im all for credible alternate histories. Im currently studying the cold war, its influences and effects on history and a thought that may not directly influence your game but is still interesting for the melting pot, could Germany have actually won against the US?

I am not pro any one side but from my research - no way in hell!

Germany take over Europe? Very credible if Hitler hadnt decided to make war on two fronts and fail at both. The Germany vs America idea is far more difficult. America had somthing like more than 70% control of the worlds economy, the worlds largest industrial base (I think Germany at full capacity was less than 1/4 of American assets), America had strong allies to draw upon eg. Britain (even though they were smashed in your version), Russia an emerging superpower with capacity far greater than Germany even after relocating over the Ural's, Russia basically won WWII inflicting more than 60% of Germanys casualties in the whole war. Germany had what? Japan? Japan was one of the worlds weakest powers, it stung the US at Pearly harbor but the US rebuilt the whole fleet and then some within two years while Japan could not replace those losses.

In short all the axis powers at full strength would have had monstrous difficulty taking America alone. Germany's advantage in war has always been superior quality of training and equipment and actually seasoned troops entering conflict rather than vast numbers eg. Russia. So Germany cuts through the enemy hordes quickly and makes rapid gains. But as war progresses and casualties mount you can't replace the experience/resources lost so Germanys performance declines.
The US on the other hand relies on mass produced hordes. As war progresses the US with its monstrous industrial base commits more resourses and its military performance rapidly rises, growing stronger as conflict continues.
In short
Germany = lightning wars of mobility
America = extended conventional warfare basically bankrupting its opponents into submission

So Germany making war on the US homeland, crossing against the US Navy to fight the industrial giant on its own soil? I can't see that as a realistic premise unless Germany has some kind of mamoth advantage, say Russia joins the Axis now Hitler is out of the way?

(Germany needs a noble Troika to lead, just like pre-war Russia :D Im thinking Rommel (the public face), Manstein (possibly the single ablest commander of WWII), and one more maybe Canaris (head of German intelligence and one of the conspiritors against Hitler). Send Goebles, Himmler and the rest to the Gas chambers, do the Moses thing and let the Jews go free and Germany is not such a nasty place.)

As to offending people, you will never avoid offending someone, but Im sort of getting sick of the rightious propaganda painted by the victors stuff. There is no evil, no good in war, only war itself.
Rant off.