My daughter has bought another home with granite counters and a drop in sink. Can a professional put in an under the counter sink in the existing hole with some modification by him or is this just simply impossible?
I hate to be a wet blanket on this one, but you are not going to like my answer. It will be very difficult to find someone that will attempt to do what you are asking for an in place, already installed granite counter top. Since you have a drop in sink, the cut out is probably not polished and the cut edges are not routed. In the fab shop, they use lasers and computer aided cutting tools to get perfectly shaped holes. Cutting in the field is hardly ever done. The process of attaching the under side bowl is not as difficult as the cutting and polishing, but will require some type of custom support to hold the bowl in place while the epoxy cures.
Depending how large the counter is, it may be cheaper and safer to have it taken out and done at the fab shop.
Yes, get a sink that is larger than the existing hole, and the installer can cut/router out the additional amount. Finding a sink that is an exact match will be nearly impossible. As well, the cutout on the existing hole is likely to be not as neat as one would like for an undermount.