Who made the string. IMO and from experience I'd say it doesn't have enough twists in it. Most of the better ones I've seen have a complete twist in 1 1/2" of string length..

Try checking the bow's axle to axle length and compare to specs. If it's long then you may be able to add about ten twists to the string. This might help stabilize it and get rid of the peep rotation. The twisting will make the draw a hair shorter and drop the poundage a little. To remedy this you add a few twists to the cables.