Rear end moving around in sharp turns

So if I weld the tubes to housing I wonder if this will correct? It’s really bad feels like rear steering . I wonder if the lunchbox locker in front is causing this ?
I found a housing on Craiglist cheap. My concern on welding would be will the axle tubes remain straight but you can bet somebody here has tried it. When you weld the metal will pull in the direction the heat is applied.