steering wheel shakes at 35 mph

Have the tires rotated just to see if the front tires are out of round or have a flat spot, because you already had them balanced and if the shaking goes to the rear then you know its the front tires

Could be tires need correct air pressure or need rotating. Sometime older tires get out of round and can be a bear to deal with in terms of vibration in steering. You may also want to check out your rotors to see if they need to be changed. Good luck!