Depending on your exposure time, the "double" moon may be due to the movement of the earth.
If you shoot any celestial object (other than geosynch satellites I guess) with a shutter speed much more than a few seconds you'll get planetary movement in the shot (yes we rotate that quickly!
). At 30 seconds it's obvious with a telephoto.
Can you describe the photo you're looking to create a little more? Moon with detail, or just a white disk? Clouds backlit by the moon or brightand puffy like we see them during the day? Clouds showing motion (time-lapse)? or static?
Without any further description, I'm thinking of a low full moon with clouds traversing it. The clouds are lit by a setting sun (so they are front-lighted and comparable in brightness to the moon). I'd go on a haze-free day, so the sky was as dark as possible compared to the clouds.