Auto transmission sometimes a bit jerky. Have changed atf and filter better. Have been to an auto specialist who says pin hole in radiator allowing glycol contamination. Is there a radiator inside box? As water level in main radiator is ok.
Most automatic transmissions are cooled through the front radiator in the car. The coolant can mix with (according to your mech.) With the tranny fluid and mess with transmission. Replace your radiator or have it fixed at a radiator repair shop.
Then have your transmission fluid flushed.