I do not know the cost but I have heard that it is done at Garcia & Garcia (Across from the Nacional Supermarket) and at Referencia, in the Centro Comercial Metropolitano (Corner of Texas and 27 de Febrero). I would also call Dr. Pedro Jorge Blanco (look in the book under Laboratorios.)
Google "adnlab" !
They are located in Santo Domingo and have the best prices and Service in the Country. They also have a Home Kit that allows you to take the samples by yourself at your Home. The owner speaks perfect english and German.
I hope this helps. Let us know about the Results will you !?
You can order DNA test online for about 100 USD. This is the home test kit. It will not be legally admissible, but you will know the truth. Later on, if necessary, you can get a legally admissible test.