The arrow problem first. Are they the right spine for the length and bow weight? Arrows spined too light will often do this. For a checl you can try turning a turn or two off the limbs and see if it improves. OR, have you spun the arrows to see if the broadhead lines up with the shaft? Crooked inserts can cause the head to seat crooked in relation to the shaft and cause your problem. OR, what fletching are you using? The fletching should have enough surface area to stabilize the arrow in flight, and it MUST be put on either straight/offset or helical to spin the arrow--same as riflings in a barrle do to a bullet and for the same reason.

As for the peep. You have a couple choices here also. Either use one with a rubber peep aligner or get a good string on the bow that will not twist as the bow is drawn. The peep is not the problem. It's the string. PM Gibblet and order a complete set and if installed correctly peep rotation will be a thing of the past along with string creep. The use a peep with a big hole such as the 1/4" or 5/16" one from G5 or the Magnum Hunter version from True Peep.