Ya gotta love people that control their kids.
Try putting some lighter fluid on a piece of soft terry cloth, then wiping
the sticker. You should get enough on it to soak through the label then lift
it gently. It will loosen the adhesive on the sticker so that you can lift
it off. When it's off, wipe again to remove residual adhesive.
you should try the fluid on an inconspicuous spot first to be certain it
will not damage the film or soak in and damage the film's adhesive.
I don't know if it will soak through or not but I DO know it removes labels
extremely well without harming paint or plastic.
Best of luck to you.