I think that one of the most striking elements about the relationship between Bruno and Kotler is how the former perceives the latter as a threat. Bruno senses that Lieutenant Kotler is inauthentic. He feels that Kotler is only interested in power and that Kotler wishes to "move in" on the home that Bruno's father is absent from with his work responsibilities. Bruno recognizes that Kotler is more interested in power and prestige than anything else. The way Pavel and then Shmuel are abused by Kotler is one reflection of this. Another reflection is how Kotler seems to enjoy showing off for Gretel, who is enamored with the image he presents.
There is evident tension between Bruno and Kotler. Kotler recognizes that he cannot sway Bruno with his prestige. For his part, Bruno recognizes Kotler as a phony and someone who is more involved with his own stature. The relationship between both does not seem to change, remaining one in which the austere embrace of Nazi ideology cuts off any chance for real human communication.