the force let palpatine know anakin was in trouble on mustafar
That I get. But how did Palpatine know Anakin force-choked Padme?
Ya know, I'll be the first to comment on a lot of the stupid things in the movie, but I suppose for this, Ole Palpy could've just read his thoughts. He did it before, when revealing himself as a Sith Lord and letting Anakin know that together they could save Padmé. Although it's debatable that he might have put those thoughts into Anakin's head.
Anyway, just as Luke's thoughts went to his sister while he was fighting Vader, I imagine Anakin's thoughts went to Padmé while he was becoming the six million credit man.