The first step in working with any family business is to get a job description. Sounds routine, but if you have clear written goals and everyone agrees about how your role is defined, then debates about what you were (or were not) supposed to do can be minimized. Whether it's a good idea to work with your Dad or not depends a lot of your relationship: when growing up could you work well with him to do chores, like cleaning out the garage? Did he ever give you compliments? Do you enjoy the kind of work you will be doing? Do you have the "right" competencies to do the job?
If you are capable of doing what he asks, there is clarity about goals, and the relationship is reasonably positive, it could work out well.
Sometimes it's hard to continue to take direction from a parent even after you have come of age, but sounds like he is the boss, the current leader of the company. The fact that your question is about Dad's "authority" makes me wonder whether some "unfinished" business will impact your working relationship - unless you work on re-defining it for the workplace.