Slava's getting sick of Kiev's nonsense. (Please ignore my inconsistent spelling.)
I think part of it is that she's worked out that she can get away with stuff like that, and that Slava isn't going to pull rank/abuse his position of power in their setup if she annoys him/is more assertive. So the sass runs free. :P
I do think that Slava and Basil would definitely see eye to eye. Say, when was Slava born? I mean the year of his birth. I kind of am interested of making a fanart with them, and it'd be interesting to keep it chronologically correct if possible.