You're right - Anakin's turn must be believable, it's key to the film working... which is why for me the whole scene of Anakin one minute being a conflicted Jedi, the next going off and murdering a load of kids is the real problem. It's totally unbelievable. If Palpatine instead tells him to go to Mustafar to kill the Separatist leaders - well that I can believe Anakin would do.

Lucas was tinkering with the 'turn' until the last minute, but he missed the real problem: the idea of Anakin killing those kids is ridiculous.