Why would his goals and motivations suddenly turn on a dime?

That's how the dark side works. It's the implication that by giving into anger and hate when killing someone that the dark side subsumes you and you fall into that pit. Anakin jumped over the edge when he killed Windu out of an emotional outburst. Anakin never wanted to destroy the Jedi order, he was frustrated with them, but he never wanted to end them. He could have simply arrested Palpatine (as was his plan 10 minutes ago) but instead decided to join him, kill his friends and lead an empire. That's a pretty big change in goals in just a few minutes.

We see this over and over where Palpatine tries to get people to strike him down in anger, he goads them on because he knows once they give into that emotion there's no coming back.