I would like to remove my single vanity light fixture and replace it with two light fixtures. I am removing a large mirror and replacing it with two cabinets. The light fixtures will be placed over these cabinets. The present light fixture is centered over the mirror. I will need to move the wiring to the two new locations. Will I need to cut through the drywall to get the wire to the new locations? The are studs between the two locations. What's the easiest way to install these fixtures?

If you gave us a drawing or picture I could be more specific but yes you will need to open the wall to get to the current box. I would actually cut out a large piece of drywall and don't try to salvage it. Move the existing box back into the wall cavity so you can later put a cover on it to seal it. Run a new piece of 14-2 out to each new box where you want your new lights and hang the new boxes from metal hangers or nail them to the studs. Now you can splice in a new piece of drywall and tape it.