The thieves guild and DBhood work together sometimes, so it's perfectly fine if you join both.
And it's not really the "imperials" that kill your whole family, it's just the Penitus Oculatus, which is basically the Blades, or the new bodyguards of the Emperor. So I mean that's up to you lol
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I thought Brynjolf once called the DB something like "mindless murderers", once. And I mean... protecting the Emperor is still being part of the Empire. Like, we go to Solitude to try and take down the Emperor, then the Empire sends their little special squad to our sanctuary. I don't know how I could side with them...
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I don't recall that, I do recall that during the emperor assassination you're sent to talk to that one guy with the Thieves Guild to appraise that necklace. Aside from that they just tell you not to kill anyone, since that's the DBhood's job Sure but that's like saying you hate the Army because the FBI killed your family