Well let's say that firstoff having "tiger-master" in your goals will certainly get your application remembered for its uniqueness!!!!
What you have mentioned in your family business sounds very interesting, and is quite well-sized, but it is not so large that I can say "you will for sure get in to a top program" (which, if you run a mining company with 5000 employees is more the case). But anyhow you have a shot. I think besides your current success, a very important part of your application (and more so than for other candidates) will be how you are able to present a clear and cohesive story for the development of this family business, and how it connects to your business school application.
1. Don't worry about your Masters. It's less important than UG and GMAT. If your grades are really really terrible then you may want to consider explaining a bit.
2. Awesome GMAT + Humanities + tiger-master???

I'd say so. But do work on it when you prepare your essays.
If you have anything else you'd like to ask, just shoot away!