for some people who confused why she called him father is because usually abeonim/아버님 (=father) is polite way to address other people parents(dad)
yerenica's soul seeing the story from the emperor's child perspective and as she said the story didn't mention the emperor name, she usually called him abeonim so its like habit.. like when we address some sub-characters with a nickname bc they didn't have name or their name is not really important to remember
and for comedy puspose too i guess, the way she address him as father its funny if you read in korean