Flip UV's is the correct tool to resolve this issue.
Here's a screen shot of a thin cube I made (like the "handle" section of your drink box). I mapped a Modeler screenshot on it. The perspective port in the upper right shows the back face polygon, the perspective port bottom left shows the front face polygon. The upper left port shows the UV map. I made a simple planar UV on the Z axis. As you can see, the image is backwards on the back face.
Step one: select the back face with the flipped image.
Step two: click the FLIP UVs button, then choose Flip U. The screen shot below shows the results.
Problem solved! Both sides now have the image mapped correctly. You don't have to flip the entire map. Just select the polygon(s) you need to flip and flip them. This changes nothing on the model itself; the flipping only occurs in the UV map.
P.S. nice to see you again. Does this mean you'll be finishing the DS9?