The set screws in the center of the axle are there to keep the axle centered in the frame. Only the right wheel is powered which also means only the right wheel brakes when operating the rear brake. This is because the rear wheels must be able to spin independently when turning because the outside wheel will move faster. Unfortunately no one builds differentials at this price.
If you have wheel wobble you need to determine if the axle is bent or the wheel is not true. Prop up the rear of the bike on a stand and remove the problematic wheel. Manually pedal the bike and check the axle as it spins. If the axle is wobbling then it is bent and will need to be replaced. If it spins true then the wheel is the culprit.
The axle is relatively inexpensive and can be ordered through a Schwinn dealer. Any bike shop should be able to true a wheel for around $15-$20.
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