I want to change out a 36" wide bath vanity to a 30" vanity because it's too close to the toilet. It needs to be flush with the bathroom side wall so that would put the center of the sink 3" to the right of where it currently is. Is there a way to connect the drain to make up this difference or would we have to move the plumbing? (If so, I'll just replace with another 36" vanity!)

That all depends. It depends on the type of trap you have. If you have a compression type trap you most likely will be able to rearrange the trap and the trap arm. A compression type trap is the kind you can take apart with your hands. If you have a glue up trap, that is a PVC trap that is glued together, you will have to cut out the existing trap and rebuild. That is not difficult and I would not consider doing that changing the plumbing.
If you have a compression fit trap and the trap and the trap arm (that pipe that goes to the wall) points directly back to the wall, you should be able to simply turn the trap to one side and reconnect it
If the trap is turned to one side and then the trap arm goes to the wall it depends on which way the trap is pointed. If the trap is pointed away from the toilet, and then trap arm goes to the wall, you should be able to simply rearrange the trap and arm. If the trap is turned to one side toward the toilet you will have change the fitting on the pipe that comes out of the wall. That fitting is called a trap adapter fitting. Most drain pipes are either PVC or galvanized iron. If you have PVC you will have to cut off the present trap adapter then glue on a 22.5 or 45 degree elbow. Then glue on another trap adapter fitting.
If the pipe coming out of the wall is galvanized iron you will have to remove the trap adapter, screw on a elbow and the put on another trap adapter. You may be able to find a screw on type PVC elbow.

Show a picture of the inside of the cabinet and the piping and indicate which side the toilet is on.