It's perfectly alright for a photo of a comet to show stars "trailing" - if trailing is what you mean with "moving".
However, DeepSkyStacker, DSS, lets you stack your comet photos in 2 different ways: one with focus on the comet (and the stars are lines) and one with focus on pinpoint stars (and the comet is a green line).
The result of both stacks you can then take over to GIMP or Photoshop and layer and mask them on top of each other so you get the good things from each and mask away the unwanted trails.
http://deepskystacker.free.fr/englis...#cometstacking