I'm confused where yo got this idea the Empire killed your family in your own home? Your character is in the process of illegally crossing the border and gets caught up in an Imperial ambush designed to capture Ulfric Stormcloak and end the war with minimal bloodshed.
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By family, I mean the Dark Brotherhood.
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My mistake. If you need a way to reconcile Empire and Dark Brotherhood I just did DB first when my character "was young, impulsive, and hungry for gold" and joined the Legion after a change of heart a few years later as he matured. I'm usually not into the whole "Role playing" thing but I did try and think of a logical character progression as my character aged and matured to give a semi-realistic reason to be a member of all the guilds and of the Legion.