I would definitely recommend round 2. Most schools actively discourage international applicants from applying round 3 because there's just not enough time to get a visa at that point. A lot will depend on your GMAT score. You're coming from a very tough demographic as I'm sure you know, and it's one that tends to have very high GMAT scores. Most Indian males coming from a tech background have GMAT scores that are 20-40 points higher than the overall average at any given school - in other words, you'll want to target scores where you are at least 20 points above the average in order to really be competitive.
That said, one definite advantage you'll have is your family business experience, and I'd consider naming the family business as your post-MBA goal too. The adcom loves family business applicants. When you've worked for the family business you've typically had the chance to have higher levels of responsibility than someone in a "regular" job and therefore have had the opportunity to drive bigger impact. Likewise, when you return to the family business post-MBA you're well positioned to enter at a more senior position than you'd have the chance to do otherwise.
There's a huge difference between a 660 and a 700 so your target schools are really going to depend on where you land with the GMAT. Assuming you hit a 700 I'd target schools where the average GMAT is in the 670-680 range (Boston University, UC Davis, etc would be a good option). If you score a 660 you could target schools in the 630 average GMAT range, like Zicklin in NYC.
I would go ahead & start some applications now & just be conservative (i.e. starting with schools like Zicklin where you'll be a strong candidate even with a 660). It will be too late if you wait to start after you have your GMAT score. Get some lower ranked school applications under your belt in this next two months, and then if you do happen to land a 700 you can use the month of Dec to get a couple more applications done in time for the R2 deadlines.
Good luck to you!