Yep I know what you did wrong in UVmapper-because I did it too.  Here is what happens, when you say make an .obj out of the entire figure and generate a texture map for it-you get everthing, the body with the face superimposed over it with the eyes superimosed over everything.  Here is what you do to get rid of the mess.  

You will notice that on your key board to the right of the "P" key you have your brackets (lower case) [ and ] the first one makes stuff invisible, the second one makes stuff appear again

First get your mess then
Go to the edit drop down list and select all
click [  (lower case) on your key board-everything will now be hidden.
 
[Now go back to the Edit menu again and  click on the select -by material.  

You will get a list of everything in the figure. Click on what you want and then a blank enlargement box will show.  Now  click on your keyboard ] bracket and it will appear.

Repeat for as many things you want to appear.  That is all there is to it--Plutom