Hello my name is Hector
Looks like you have replaced almost all the items on the vehicle. By the way you are describing the issue when you hit the brake the entire engine and all shake. I take it you have already done the preliminary checking for any loose parts in the suspension and all the rotors are not warped. I would really look into the vacuum assist of the brake booster. If the booster is leaking when you press the brake pedal it creates a HUGE vacuum leak that would be the same as disconnecting a vacuum line. Try looking at that first.
They way it works is that the master cylinder is mounted onto the booster. When you push the brake pedal the master cylinder using Vacuum form your engine will multiply the force and assist with braking. If it is leaking when you press it the vacumn that your vehicle is producing is leaking out. Think of it as pulling off one of your vacumn hoses off the carburetor it will start shaking like a champ.Look over the hose to make sure not leaking. If the rotors are new that does not necessarily mean they do not have to be turned. If the steering wheel is shaking have them double check maybe even turned. If the entire vehicle shakes feels like the engine shaking, then check the booster and the hose to it.
One more thing you may want to look at the drums in the rear. If they are warped will also cause the vehicle to shake the body. You can check the booster and the vacumn line by pressing it all the way down if it causes a leak the engine will shake.
Here let me start from the top I will document all the things it could be and all the things that it may be.
If the vehicle when braking is shaking and the wheel shakes then the issue is in the front end. Start by checking the rotors, even though they are new out of the box them may need to be resurfaced. Also check the calipers to make sure one is not binding and causing the vibration. Second check all the ball joints and bushing in the front end if one is loose this will cause the shake through the front end and steering wheel.
If the vehicle is shaking and you feel it in the pedal or on the seat and rear of the vehicle then the drums may need to be resurfaced. Have them check all the hardware and make sure that all the drum system is in working order. This may be a stretch but since you have tried everything look over the differential make sure any bushings and the rear suspension are all tight and nothing has play.
If the entire vehicle shakes then you may have a torque converter issue. Even though it was checked previously may want to try the check provided above. What happens is that the torque converter when braking will still be cranking away and causing the entire vehicle to shake. When you make it shake kick it into neutral if the vehicle stops shaking then that will condemn the torque converter.
The booster can only be checked using a vacumn pump, you pull a vacumn and it should hold. Also check the hose to make sure that it is not dry rotted. The valve should be on the side of the side of the booster and should have a huge vacumn line to it.
Other than that the only thing you can do is recheck the mounts and all the items previously checked something had to have been missed. You stated that the carburetor need to be addressed it may also be contributing to the issue but it is highly unlikely it would make the vehicle stall.
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