Auto gear shift in high revs

[metellica]

I own a Mini Cooper R50, 2004 make, 1.6 lt engine with automatic transmission.

The automatic transmission also has Sport mode and manual (+/-) modes.

Recently, I encounter problems with automatic shifting. It began to appear a month ago.

I put the gear in "D" and apply mild throttle. The car starts accelerating but gear shifts occur in high revs (4000+) although I apply mild throttle. Since the gear shifts occur at high revs, the car shakes/rocks during gear shifts. In the past, it used to shift around 2500-3000 rpms under mild throttle.

Additionally, when I step my foot off the gas, the car tends to instantly downshift and, as a result, the rpm increases and stays high until I come to a full stop. Till the car stops, it shakes back and forth, similar to the case during acceleration. I haven't experienced that before.

In order to resolve the problem, I had the "lifetime oil" of the tranny changed. It did not resolve the issue.

The car's fault memory is also checked, but, unfortunately, no fault code or clue about what is going on.

Which unit controls the gear shifts in automatic transmission? ECU? Tranny Internal Control Unit? Solenoid? Does anyone know that?

What else should we check or suspect?

Any ideas would be appreciated. I really need help in that.