BMW X3 transfer case problem

Shudders on X3's are pretty common, ours has had it for years now. We replace the transfer case fluid regularly. We have come to accept it as standard. It is usually worse in colder weather. The only thing I would say about the tires is to keep them inflated to spec as shown on the door jamb. It is really important for all four to have the same treadwear and air pressure (this applies to any AWD vehicle though). For it not to be a BMW approved tire I think is rubbish.