Car Shakes When Braking
When the entire car shakes when braking the only possible reason is the rear drum and the rear brake shoe is maligned, when those two components is not align with each other the shaking affects the entire car.
Rear Shoes and Drums is Misaligned
Usually when the entire car vibrates when the brake is applied, this means that there is something wrong with the rear brake.
What is happening here is that the rear shoes and the drums is not aligned to each other and is not even contact during brake application. If those two parts is misaligned it can cause vibration. Now, why is it that the shoes and drums are not aligned?
Usually the most common cause of misalignment is a warped rear drums. It is also possible that the rear drums is good, if this is the case then the problem is the rear wheel bearings. The bearings are already worn out or loose. A bearing that is worn or loose can cause an indirect misalignment between the shoes and the drums.
Bring the car to a reputable car shop and ask the mechanic to first check the rear bearings for any looseness or worn. If the rear bearings are in good condition, the next thing to do is to have the rear brake drums machined so that the warpage of the drum will be corrected.
Once the drum is corrected, you need to replace the brake shoe because it will not be aligned well to the corrected drums it is necessary for the machined drums to be fitted with a new shoes so that both parts will have even contact with each other during brake application to avoid car shakes when braking.