Shaking and rough driving after hard acceleration

I drive a BMW 530I (E60) model 2006. It has automatic transmission with steptronic.

The problem I have is that when I accelerate hard on automatic (gear changes happening above 4000 - 5000 RPM) I get lots of power but when I lift off, the car quickly and sequentially up shifts to the appropriate gear and then shudders a lot upon my pressing the accelerator. It feels like quite a loss of power at that time. If I do keep it floored, the shuddering in less at higher speeds. This continues for a few minutes and then goes away, or goes away if I immediately stop, switch off for a minutes and then restart the car.

If I do not accelerate hard, there is no problem under gentle acceleration (shifting automatically at about 3000 RPM).

The issue first appeared about 6 months back and the dealer told me that they would change the spark plugs and take it from there. The spark plugs were changed but the problem reappeared 2 months afterwards (very intermittently) and have not been back as I did not know how to reproduce the issue till about 2 weeks ago, i.e. now I am sure it will shudder when pushed hard.

Any advice would be welcome as to what could possibly cause something like this, as I wanted to be a bit more knowledgeable before I go back to the dealer.

Cringing at the thought of getting a large repair bill, so I really want to have enough knowledge not to be gypped.

Thanks in advance.

Update:

I tried the "25s gas pedal press trick" that I found on the forums. It was supposed to help with jerky transmission shifting, but I thought it wouldn't harm anything to see what it does. The theory was that this trick resets the transmission control and makes shifting smoother

I drove the car after that, and accelerated three or four times up to 5000 plus RPM, and wonder of wonders after I lifted off, the car up shifted as it should, and when I floored it again there was no shuddering

I do not know whether it's a permanent fix, but if the shuddering was only due to the transmission wondering which gear to upshift to upon second acceleration my problems may be over.

Fingers crossed.