Anakin wasn't all submissive all of a sudden. It was thought out, he made his decision when he left the Council Chambers. He would rather watch his friends die than ever lose Padme. He solidified his decision when he protected Palpatine from Mace.
"I will do whatever you ask, just help me save Padme's life."
"Uh...yeah, listen - we COULD save Padme, but first we JUUUST gotta figure out how. In the meantime, kill all the Jedi in the Temple...only then will you be strong enough to save Padme."
Anakin's mind was made up when he walked out of that Council Chamber to save Palpatine. Whatever it takes, I'll do it.