I made contact with all the children I sponsor in the DR, and send them stuff on a regular basis with their parents consent, I think they become more relax once they get to know you a little bit better before you show up and all that, never the less I spoke with a rep from the Org. and explained that you're going to visit the DR for vacation and they were sure they could accommodate you in short notice always that a rep was available in the area the child lives at the time of your visit, she explained to me that they have a very small staff there.
Try and call them a second time and explain that you're visiting DR on vacation and would like it very much if they could arrange for you to pay a visit to your sponsored child, by the way, have you had correspondence with your sponsored child before?.
As far as to enroll a child on the program it could be arranged always that you understand that they have a limited staff and the program is not on the national level, they try to target the poorest and more in need first before they can help others, it sounds a little hard but it works for them, I don't see why you shouldn't be able to have this child join the program always that they offer their program close to where he lives and can obtain their parents consent.
Hard work always pays a good reward, so try a little bit harder.