If you are absolutely convinced that you want to ship your own car down here instead of buying one here already, I have always found it best to use a reputable car dealer to handle the transaction for you. They do this every day and know all the ins and outs.
They will tell you exactly how much it will cost you BEFOREHAND and you can decide to go forward or not. Of course, they will charge you a fee. Yet this will be much less than the grief you will encounter on y our own. You can choose the dealership of your choice, I have done this in the past using Espaillat Motors (809-578-0162) in Moca, they are one of the largest car and suv dealerships in the Cibao region and have affiliated dealers in New England and in Florida.
Disclosure: I am not affiliated in any way with this dealer, just my experience as a paying customer. You can do a little research and find a reputable dealer of your choce, as well. The bottom line is having as much information as possible before you go ahead with your plans.