First, welcome to DR1!
Second, some variant of your plan is posted a few times a week here. People regularly fall "in love" with the place (and often, a person or the overly permissive lifestyle), and start making plans to move to DR while they're still on the flight home.
The reality is, it's extraordinarily difficult to make a living in DR, particularly in the touristy areas. Even if you successfully naviagate the challenges of doing business and find a niche where real demand exists, in the event you are successful, you have to deal with copycat businesses popping up within days. Next door.
Which means whatever you do must have a real barrier to entry. It has to be expensive (like purchasing property, boats, motorcycles, etc), have a clientele that is marketed to while they are still in their home countries, or be something that simply can't be replicated very easily.
Unfortunately, T-shirts and cell phones don't fit that description, and most tourists aren't looking to put together some tracks while on vacation, so you will likely have a very difficult time.
My advice is to build your business in the US, and develop online skills where you can work from anywhere. The fact you have family living in DR is very helpful, but I would also encourage you to read this thread, which will give you a sense of how much it costs to enjoy a NA-EU level lifestyle:
http://dr1.com/forums/living/112283-living-costs-dominican-republic.html
Best of luck!