You need to maintain your balance throughout your entire swing sequence, this requires the torso and arms moving together allowing you to maintain your center
Although an unconventional swing, emulating Lee Trevino's swing by focusing on his right side and the way he came down and straight through the shot, tracking the target line, is a great idea
Practice hitting long putts with just your trail hand in order to get a feel for the putter's flow and eliminate hip action in your stroke