Any reputable lab can do the testing. Check with these:
Lab. Dra. Amadita Pitaluga de Gonz?lez
They have 7 locations in Santo Domingo. Call 809 227-6633 for the nearest.
Laboratorio de referencia
6 locations in Sto. Dgo. Call 809 472-1990
Dr. V. De Sanctis
2 in Sto. Dgo. Call 809 412-2696
All these I have used in the past (although no for paternity tests), they are very good.
Good luck