differential problem when turning

What you more thn likely have is a transfer case stuck in 4hi lock. There is a plastic mode fork in the transfer case that wears and creates this condition. You may hear the case shifting between lo range and hi range, but your 4hi limited, and 4hi lock is the concern. What is happening is the front and rear wheels are trying to turn at the same speed. When in a turn the front turn faster due to difference in radius. On slick surfaces, this is not noticed, when there is traction like wet/dry pavement is when you notice it. You may also feel feedback in the steering wheel, a condition known as crow-hop. What needs to happen is the transfer case removed, and the covers split. The fork needs replaced, and possibly the collar that the fork interacts with.

I have exactly the same problem with my 2006 H3
- in a shop they said first of all the computer has to be flashed, is that true?
- also that in the Tcase is replaced the computer has to be reprogrammed, is that true?

Is there any codes? Lets run the computer to see what comes up. here is a guide to help:

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Please run down this guide and report back. The computer may or may not need to be updated/flashed we will see after the code scan.