Was Palpatine using some kind of mind trick/dark side trick on Anakin. It seems like at times he would change his voice or have a deeper dark tone when Anakin wouldn't listen to him.
I don't think so. I think fans have a tendency to blame Palpatine for every negative thought or decision from the other characters.
He was being that father figure that, other than Obi-wan, Anakin never had. He listened to what Anakin wanted in his fits of rage and convinced him to give into those needs.
I like to think it's Palpatine letting a bit of "Sidious" out of the cage. Darth Plagueis even mentions that Sidious had grown into the habit of slipping on the "Palpatine persona" effortlessly...so maybe it's intentional on his part?