^We really don't have much of a baseline of Dooku's character prior to becoming a Sith Lord to make any meaningful comparison, let alone guess at what his intentions were before meeting Palpatine. We don't even know the circumstances of that meeting.
Personally, I think it would cheapen Dooku's character to say put all the blame on Sidious. He's a sneaky manipulative bastard, but there's only so much influence he can have, especially on a Jedi Master. Indeed, neither Krell nor Barris seemed to need any direct influence from Sidious to turn them against the order. They're all as responsible for their own actions as Anakin was.
We do know that Dooku comes from nobility and the impression I'm left with is that he was taken by the Jedi when he was just old enough to remember it. Perhaps enough that it instilled in him a deeply rooted sense of privilege and an inclination toward authoritarianism. That would potentially lead to a distaste for the Senate's ineffectual leadership and the High Council's passivity in a clearly stagnating galaxy.
That said, it's hard to credit the notion that Dooku was ever truly concerned with the well being of others. Most of his interactions make it clear he has little to no respect for anyone besides himself and his Master and even that is only because of Sidious's considerable power. He thinks he has the right to rule, that he knows better simply because of who he is. An arrogant delusion suffered by all forms of aristocrats.
Given that he appears to have been a stop-gap after Sidious unexpectedly lost Maul, I think it's a fair guess that Dooku had already left the order and was well on his way down the dark path when Palpatine made him his apprentice.
There may be reason to think Palapatine was already using him as an asset prior to this, but that only supports this proposition as it means he was already close at hand, so to speak.
