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Have you checked the engine and transmission mounts recently?
Has the vehicle been serviced, spark plugs etc?
Coolant and transmission fluid cross contamination will cause transmission shudder and ultimate transmission failure if not addressed.
The radiator transmission cooler cracks internally.
Trans fluid pressure weeps into the cooling system.
Hot coolant under pressure weeps into the transmission, once the engine is shut off.
I would get a trans fluid sample, and a coolant sample for analysis.
Then replace the radiator if contamination exists.
Flush both systems afterwards.
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I hope my advice has been of assistance to you.