I agree with Valerie. In addition, using "must" usually conveys some sense of obligation (and often not one that is desired by the speaker). So the speaker in your example sounds to me as though they do not wish to go home but are willing to accept the duty or responsibility if the answer they receive is yes, they must go.
Also, typically one would just say "Must I go home..." (again, as Valerie shows above). The phrase "to the home" would be considered a strange way to phrase that particular idea in English. By way of contrast, "to the house" (meaning the actual structure itself) is perfectly fine. In English "house" typically refers to the physical structure whereas "home" is more often used in a more personal and emotional way to refer to the place where one lives (that is, it conveys a stronger sense of belonging to that place).
I hope that helps!