What is your family business? Generally MIS is a major that scales well for large scale companies. Is your family business considered large scale? and/or is it computer related?
Keep in mind, MIS majors were created to help tackle the enormous tech challenges that were arising. Many of the demands for tech/IT companies may or may not be directly relevant to the "computer technology" learned in the MIS major. If you're talking about the latest web technologies, for example, these are not covered in MIS majors as schools are generally 5+ years behind the latest in technology. Working with PHP/MySQL databases or Ruby/Python are things that MIS won't cover - they'll focus more on the corporate side rather than the new age web tech stuff.
So if your family business is somewhat large tech-related, an MIS concentration can be directly relevant. Otherwise, you'll want to see whether you wish to leverage that MIS major to get your foot in the door elsewhere.