I've been trying to learn songs that have a main "sound" with moving bass line, such as songs by Tommy Emmanuel and others, but something is hindering me.

I have this tendency where my thumb does what my other fingers do, or vice versa. Take for example, the arrangement of Daytripper by Tommy Emmanuel (A powertab can be found on ultimate-guitar.com) The song calls for a moving bass line with an accompaniment that goes by quarters, played by the rest of the fingers. I can't maintain that accompaniment's rhythm when I play the bassline. Rather, I have the tendency to either speed up the accompaniment to playing by 8ths or just stopping then resuming once the bassline slows down.

I also have this problem with both hands, where one hand tends to do what the other does, which is why I thought piano was hard.

Is there any good ways of getting rid of this habit?

Also is there some special way of using a thumbpick to avoid the bass notes from overpowering the other notes?