If it's a completely parallel relationship, I'm guessing daemons only say 'mother' and 'father' when referring to the daemons of their human's parents, right?

Yeah, I thought about that, too. The situation is that Thor is getting told off by Frigga in public with Runi and Svana playing go between to keep it discreet, so I couldn't decide if it should be 'Mother says to behave yourself' or 'your mother says to behave yourself' or 'Frigga says to behave yourself' or 'Runi says to behave yourself'. Since we don't really know how daemons come to exist, it's hard to know if they consider themselves related to their human's parents or not. My own head canon is they sort of burst into existence shortly after a baby is born and takes a first breath.