Sway and jerkiness in the 2011 M Sport 3.0d E70

[developer]

Good day. My new tow vehicle was just delivered. 88k miles, great SH, just serviced 8-speed gearbox, and new transfer box. Aside from a bothersome juddering sound that only occurs when it becomes heated (which happens after around 20 minutes), I'm really satisfied with it. While accelerating from 10–40–50 mph, there is what feels like a sudden stutter and lurch. If you're cruising at 50 mph or more, it will smooth out. It will go into high gear at some point. To illustrate, let's say you're about to enter a roundabout, slow down for the turn, and then jerkily accelerate out of the roundabout.When this occurs, it usually goes something like this. My recent checkup at an independent clinic came up clear of any health issues. Are we considering issues with the engine's EGR, MAFF, and gearbox?as well as the torque converter. Very irritated because everything else was great. I would appreciate any advice you could give me.

[guyskin]

Are your tires in good condition? Make sure the tread is even on all sides because an uneven tread can cause problems with the transfer box.

[developer]

Much obliged. Your tires are in good condition. Great tyres with lots of tread.

[CheresX]

Does each tyre have the same tread depth? That was my question.
Unfortunately, most people only install two tires at a time, which can cause serious damage to your car's transfer box.