Thank you for your question! First, a correction: You and your father ARE in the house. ("are" because it is plural.)
Father and Dad are interchangable in meaning, however, Dad is less formal. I do not know if that answer above from Nanren888' in New Zealand means that parents are called by their names refers to their first names. In the US, it would be extremely rare to call a parent by their first name (George or Jose). In fact, it would be viewed by many as disrespectful.
Dad is more often used by the child, regardless of age. Father would be more common when introducing your parent formally as in "Professor Sandy, I would like for you to meet my father Dr. Washington." In casual conversation with friends, Dad would be used as in "My dad and I went to the movies on Saturday."
Please let me know if you have any more questions. Keep up the good work!