I attached the steps for removing and replacing the differential housing below for you.
https://www.youtube.com/watch?v=kLBxcXzyKYg
I also posted the steps below for the replacement.
Most repairs do not need to replace the housing as the interior of the differential can be rebuilt for less money than replacing the housing itself.
https://www.2carpros.com/articles/how-a-differential-works
Roy
Rear Axle Housing Replacement
Removal Procedure
1. Raise the vehicle. Refer to Vehicle Lifting.
2. Drain the axle lubricant.
3. Remove the rear axle assembly.
4. Remove the brake caliper brackets.
5. For the 8.6 inch and 9.5 inch axles, remove the brake rotors.
6. For the 10.5 inch and 11.5 inch axles, remove the hub and rotor assembly.
7. Remove the rear axle cover housing and gasket.
8. Remove the axle shafts.
9. Remove the brake backing plates.
10. For the 8.6 inch and 9.5 inch axles, remove the rear axle shaft oil seal and the bearing.
11. Remove the differential assembly.
12. Remove the drive pinion shaft yoke and the oil seal.
13. Remove the drive pinion and the inner pinion bearing.
14. Remove the pinion bearing cups.
Installation Procedure
1. Install the pinion bearing cups.
2. Install the outer pinion bearing into the axle housing.
3. Install the drive pinion oil seal.
4. Determine the selective shim thickness for the drive pinion.
5. Install the selective shim onto the drive pinion.
6. Install the inner pinion bearing onto the drive pinion.
7. Install the drive pinion.
8. Install the pinion yoke.
9. Install the differential assembly.
10. Adjust the differential side bearing preload.
11. Adjust the drive pinion to ring gear backlash.
12. Perform a gear tooth contact pattern check.
13. Install the brake backing plates.
14. For the 10.5 inch and 11.5 inch axles, install the hub/rotor assembly.
15. For the 8.6 inch and 9.5 inch axles, install the rear axle shaft bearing and the oil seal.
16. Install the axle shafts.
17. Install the rear axle housing cover and gasket.
18. For the 8.6 inch and 9.5 inch axles, install the brake rotors.
19. Install the brake caliper brackets.
20. Install the rear axle assembly.
21. Fill the axle with lubricant. Use the proper fluid.
22. Lower the vehicle.
Monday, October 12th, 2020 AT 6:16 AM