Parking, even with a twisted preload, should not cause the wheels to retain a distortion. They may appear to have distorted while parked but once you move the trailer the wheels should settle out. As noted above the wheels are designed to flex to reduce tire scuffing as the trailer is being turned.
If you have move the trailer and the wheels still show visible misalignment there is a problem more than likely in the axles. If this is the case find a truck axle shop for the realignment. These axles require bending to correct any misalignment. and that is something that requires a special shop. Do not take the trailer to JC for this work.
WBCCI 12156 AIR 3144 WACHUNG TAC NJ6
2004 Excursion 4x4
1991 34 ft. Excella +220,000 miles, new laminated flooring, new upholstery, new 3200 lbs axles