Ok, I think I'm not really expressing myself clear enough. In the beginning only my desktop worked, both laptops not. Then I did what you said on both laptops. After that it worked on my desktop and one Laptop. I did the same thing on the other Laptop but for some reason I still can't access private shares. When I go to the credential manager there are no credentials displayed anymore but the "map network device" function is acting the same way it did on the first Laptop (which works now) when there still were credentials. But I double checked that there are no credentials on the second Laptop.
The only difference between those Laptops is, that they access different shares: Desktop accesses privat share A, Laptop1 accesses privat share B, Laptop2 accesses privat share A.
I hope this further explanation helps!
But thanks anyways for the help you gave me already!