PNJSNAK:
The area you put the silicone on is one of the factory welds where the parts are welded together to from the housing. With your lower link attached so close to the area where the tube goes into the housing, the twisting forces are concentrated in that area as the pinion gear attempts to climb up the ring gear. The harder the launch and stickier the tires the more this will be agrevated. As far as welding it in the car, I would caution against it. The area it is in will require a fair amount of heat to get a good weld and it may need to be checked for straightness when completed. The
oil present will contaminate the weld.
Prior to actually welding it, drill a 1/8" hole at each of the crack to prevent it from continuing to crack then weld it with a good rod, and plenty of heat, being sure to get good penetration on the weld. When you have it out, if you decide to do it that way, it would also be a good idea to keep the gear housing assembly (pumpkin) bolted in the housing to aid in keeping it structurally correct.
I was unable to tell from your pictures but if you are not already consider using urethene mounts on the ends of the lateral links that locate the axle housing, they will absorb a minute amount of energy and could prevent this from happening again.
Rick..................