Hello,I will be glad to try and assist you with this,Welcome to Just Answer.
What can cause this problem when braking is the brake rotors being warped,if the rotors are warped then when you press on the brake pedal you will get a shake/vibration or shimmy and this can usually be felt through the vehicle and possibly in the brake pedal and steering wheel.
The brake pads may have been checked but the rotors would have to be checked for any kind of warping and turned by a brake lathe or replaced to correct this concern.I have seen this problem quite a few times and in most cases having the rotors turned on a brake lathe or replaced will correct it.
Usually your transmission wont cause this unless the torque converter solenoid was sticking but in most cases the vehicle would stall out if this was the case.
O.k.,this can be caused by the brake fluid being low but if your brakes were checked then most likely the fluid is ok.
Another component that can cause this is the mastr cylinder mounted to the brake booster on the drivers side underneath the hood on the firewall.This may need to be replaced to correct this failure.You can also get a noise from the master cylinder if one of the cups inside of it are failing as well.
The parts can cost anywhere from $150 to $400 depending on your location and where you purchase the parts at the high price would be a dealer purchased part and the low price would be an after market parts store.
Labor to replace including bleeding the brakes is 1.1 hours.
I would have this double checked just to verify that you do in fact need the master cylinder,my parts book doesnt give me this option,one may for vehicles with abs brakes and the other may be for vehicles without abs brakes,a parts store or dealer might be able to help better with the right master cylinder.
I hope this helped,Thanks Pete!
If you hear the popping jerking noises when braking then most likely this fault is within your brake system as generally the transmission wont make this type of noise or problem unless the motor mounts are broken that support the transmission and engine,this could be a possibility here.