I am not positive but it sounds like you are talking about the rear subframe bushings. i had to replace mine, but luckily we had the correct tool for the job and it only took about 30 min for both. the tool is about $300. there was a lot of talk of how to do this without the tool last week. might want to do a search for sub-frame bushings
hope this helps
~artie

Thank you artie so much.
I suspected that thing is called sub-frame bushing, but i wasn't sure. Do you agree that if this thing is damaged and has extensive play it can give the symptoms i described?
Artie, if you so kind, can you please describe me the idea how this magic tool for $300 works. Because when i started to think about replacing it, i was in despair - the only think to do it is to disassembly the whole rear end.
And anyway what is the purpose of that bushing - is it some kind of additional amortizer?
And at last, may be you know the BMW part # of this bushing?
Thanks for any help in advance.
Boris Pitel