I always thought of Snivley as more along for the ride than anything else. Looking back at Blast to the Past as my main inspiration for this theory, remember when Robotnik and our little buddy were launching the Destroyer? Robotnik seemed elated at the prospect of finally putting his best laid plans into action, whereas Snivley seemed, to me at least, as though he could really care less. Let's take a step back into our SatAM history shall we? The coup happens some month in 3224 (on the 13th) and it is more than safe to assume Julian and his nephew have been living amongst the king's subjects in Mobotropolis for quite some time. At least enough for Julian to have gained substantial power and clout, as evidenced by his theft of the Robotosizer plans and his would be appointment as Minister of Science, a title that should have probably been given to Sir Charles by all accounts, but more on that later. Anyway, so we've established a bit of a base line here for happenings with Julian and Snivley within Mobotropolis. I would say it would be safe to assume a period of at the very least a year had gone by, and in all this time, as Julian's been acquiring more and more power, what exactly has Snivley had to do? That's right, not a damn thing! It stands to reason that, while Julian had all the authority, Snivley was taken care of alongside his uncle. He most likely had residence within the city, with Julian at least if not on his own, who I may presume had some rather spacious quarters given his substantial contribution to the war effort (the king credits him as having won The Great War). This may be a wee bit of a stretch, but why would Snivley want to give that up? I'd say it's more than likely he lead a rather cushy life in public at least. The coup would take all that away from him, and somehow I think he'd be opposed to that, but powerless to do anything about it.
Fast forward ten years or so, to the year 3235. Robotnik has complete control over most of the planet, exerting more force on his nephew than ever as the only living being on the planet that doesn't want his neck (as far as he knows). Snivley in turn sees his uncle eventually losing out to the resistance due mostly to his hubris and pride. He may feel he has something to prove, to show Julian that he's not as weak and useless as the dictator has always believed. However, he's overzealous, and quickly bites off more than he can chew, being almost instantly ousted by Nagus (who you'll recall was the supposed owner of those glowing eyes at the end of Doomsday). Now powerless and alone, and with the sudden realization that he's free to make his own choices potentially for the first time in his entire life. Colin "Snivley" of House Ivo returns to form as an unlikely ally for the Freedom Fighters, using his vast knowledge of the information systems still present within Robotropolis to aid them in overthrowing Nagus and his uncle.
That's something like how I think it could go...