First, I don't know why the competitive factor of business school or the potential of not getting a high enough GMAT score would influence your decision on whether or not to even try. If you want something, you have to go for it, especially since the most you will possibly lose is "a little bit" of time. So before worrying about GMAT scores or the like, you need to be make a commitment to yourself, or choose not to follow the path at all. Going about it half way is just a really bad idea and will probably waste your time and get you nowhere. If it's something you want, then go for it, regardless of the challenge. If it's not worth it, then forget about it.
I met several applicants who were planning on going back to take over their family business. They seemed like really strong candidates and I think your circumstances would give you a really good position to apply. For somebody like yourself - and I think there would be many who would love to be in your position - an MBA seems to make a lot of sense. It can open your horizons to take the business in expansive directions you never thought possible. It will also free you of falling prey to business "experts" who might try to leverage their so-called expertise in their own interests (and against yours).
Just ask yourself two questions:
1) Where do I want my family's business to be in 20 years?
2) Will an MBA help me achieve this?
You will need to answer these questions anyway if you plan to apply, so you might as well start now. You might not realize it yet, but answering these two questions will be the hardest part of your entire application process. Best of luck! Many wish they could be in your shoes.