Shudder

The best suspect is the transmission's torque converter clutch. The clue is the forty mph.

The torque converter is the fluid coupling between the engine and the transmission that allows the engine to remain running when the vehicle is standing still, in gear. It starts to become efficient at around 1000 rpm, but that slippage always exists while you are driving. The lock-up clutch eliminates that slippage to achieve better fuel mileage, similar to what a manual transmission's clutch would do.

That lock-up clutch cannot be allowed to engage at lower speeds, and when it does engage, it has to do so gradually to avoid causing a harsh clunk. Most lock-up clutches begin to engage gradually between thirty five and forty five mph. It is cycled on and off very rapidly to modulate its engagement, but there are special additives in the transmission fluid to allow it to slip at first. The most common cause of this shudder is using the wrong transmission fluid. Without the needed additives, the clutch engages too hard, then engine torque causes it to break free, then it locks up again, very rapidly.

To prove if this is the cause, when the shudder occurs, hold the accelerator pedal perfectly steady, then lightly tap the brake pedal with your left foot. That will cause the lock-up clutch to disengage for a few seconds, (in preparation for coming to a stop), then the shudder will occur again when it engages. If you have a tachometer on the dash, if you tap the brake pedal at higher speeds, you will see engine speed increase about 200 rpm. That is due to the lock-up clutch releasing. It also releases at wide-open-throttle, (for more torque), and it will not lock up until the engine is warmed up. That is to insure the transmission fluid is warm enough to flow easily to the cooler.

You are making this way too complicated. If my suspicion is correct, you need to replace the transmission filter and fluid, and use the correct fluid. If you can put up with the irritation, have the normal transmission maintenance service performed at the scheduled mileage.

Diagnostic fault codes are set when the computer detects a problem when it performs various self-tests. A majority of those tests are for the integrity of an electrical circuit. Next, it expects to see signal pulses arriving from certain sensors at specific times. Then it compares various signals to each other and to operating conditions to determine if they are correct. The computer will turn on different circuits, then in some cases, it will look to see if the expected results occurred.

There can be dozens of computers on a vehicle. A large percentage of them can detect defects and set fault codes. The engine computer can detect almost 2000 different defects. About half of those defects could have an adverse effect on emissions. Those are the codes that turn on the check engine light.

Safety systems such as the anti-lock brake system computer and the airbag computer have their own warning lights. Fault codes in other computers do not turn on the check engine light.

Most electronically-controlled transmissions use a version of Chrysler's original design. That uses an input speed sensor and an output speed sensor. The transmission computer knows which gear it has selected, and the gear ratio, so based on the input speed, it expects to see the output speed at a specific speed. If the two do not agree, the computer knows slippage is taking place in a clutch pack. A fault code can be set for that. For the torque converter lock-up clutch, the input speed sensor comes after that. The clutch packs in the transmission are what are monitored by the input and output speed sensors, but they are not what are slipping for your shudder problem. The chattering lock-up clutch is between the engine and the transmission The slippage there is what you are feeling, but that is between things that are monitored by either computer. Also, the only way the shudder can occur is if the clutch is being applied by the computer, and for that to happen, the circuit that runs the solenoid has to be good. If there was a break in the circuit that prevented the system from working, that would have been detected and a fault code would have been set. That fault code would be in the transmission computer, but since it would result in decreased fuel mileage, it would increase emissions. For that reason the fault code would be transferred to the engine computer, and that computer would turn on the check engine light.