My take on this is slightly different from Victor's.
Adcom are aware that it is common in family businesses to involve children fairly early on as an important learning experience, and also for trusted family members to be much more involved at an earlier age than 'outsiders'.
But adcom are also aware that at age 16, you were presumably a full time high school student, with any family business involvement secondary to that.
Even purely from a time perspective, it would seem infeasible to be DEEPLY involved in vision, active management, R&D, and being an outstanding student. The reader is probably going to conclude that the extent of your involvement at such a young age in so many areas is at least somewhat exaggerated.
And the problem with exaggeration is that it can really cheapen the currency when it comes to other more significant experiences elsewhere in your application.
My advice would be that rather than writing about the breadth of your involvement, select one area where you were more deeply involved, and go into more detail on that specific aspect.
Also, you may want to consider the language you use here. For example, R&D implies a fairly technical process, with complex and advanced technologies, scientific testing, etc. Even in family businesses, 16 y.o.'s just don't get let loose to "lead" this stuff part time. However, less complex companies still have the need to evolve their products and services - if you call it "new product development", you will probably have the reader more on side, and probably give them a more accurate idea of what you were doing. And if you did spend your summer's working in a genuine R&D lab, then write about it - but a summer working on a project in an R&D lab is not "leading".
Bottom line: Don't understate what you were genuinely involved in, but be selective in what you write, and focus the reader's attention on what you were more DEEPLY involved in. Family business types are often passionate about their business, and it is often a key reason for wanting to do an MBA - and even if it was originally from your teenage years, if this is important in your development, then write about it.