No, you got it pretty much exactly right and put it very well for a short explanation. That is it in a nutshell, though I would say Yingluck's attempt at amnesty for her corrupt brother (which was her and her PTP parties goal all along) was the initial trigger that brought the Yellow's back out on the street.
It sounds like you live or travel to Thailand a lot to have such a firm grasp of the situation. I was living in BKK when Thaksin was elected and still visit regularly. Was there this January when the 'Shutdown Bangkok 2014' protests were in full force. Let me tell you, getting past the Asok intersection was a nightmare. One night I was trying to get up to Soi 24 going through the checkpoints and Yingluck declared a state of emergency. Troops running up and down securing the skytrain and other key areas was a bit intimidating. The good thing was it drove the police back who the protesters don't trust because they view them as in the pocket of Thaksin's goons. A few weeks later we had pointless elections that were annulled and the whole thing has simmered since. I really think that Yingluck might have rode this thing out, but the constitutional court tossed her out leaving the current vacuum and an opportunity for Suthep to demand reforms before the next vote.
We just got off the phone with relations in Northern Thailand. Thaksin supporters are arming militias in Chiang Mai and Phrae. These are the guys that went to Bangkok and burnt the World Trade Center Mall and other malls and businesses down. They are intent on bringing Thaksin back as a authoritarian leader and taking revenge on their enemies. We have relatives on both sides.