You need to reduce your cognitive load. The other answers have some good ideas, but here is another quick one:
Simplify the picking pattern you are practicing with. So instead of practicing an arpeggiated pattern, just pluck the bass with your thumb, then three treble strings at once with three fingers held together. That's it. PLUCK-twang, PLUCK-twang, PLUCK-twang, PLUCK-twang.
That should get your right hand used to moving the fingers and thumbs differently (rather than as a unit as it is when using a plectrum) at a very basic level.
Then try the chord changes. I think that your desire to change chord after playing the first string of the pattern is not letting a rhythm set in to your right hand. I would do it to four beats:
C
PLUCK-twang, PLUCK-twang, PLUCK-twang, PLUCK-twang.
G
PLUCK-twang, PLUCK-twang, PLUCK-twang, PLUCK-twang.
Etc. etc.
