In the deleted scene a battle in Nornheim is referred to and Loki has to veil them in smoke to ease their escape, so that would indicate a combative relationship with those in Nornheim despite being part of Asgard.
also, see this: http://marvel.wikia.com/Nornheim
Although Nornheim lies on the Asgardian land mass within Asgard's own dimension, and although Karnilla is apparently of the Asgardian race, she does not consider herself to be subject to Asgardian rule. Rather, Nornheim is an independent country, of which Karnilla is absolute monarch.
Karnilla lives opulently in the ancient fastness of Nornkeep, attended by her servant, the aged minor sorceress Haag, and troops of guardian demons. Although there are many demons among her subjects, Karnilla's realm is also populated by humanoid immortals, just as is Asgard proper.