Can I file a order to stop my soon-to-be ex-husband from having his girlfriend around my daughter?

Probably not.I know that this must be awfully upsetting but unless you can prove that either the girl friend poses some sort of harm or danger to your daughter in some way or that it is adversely effecting her then I doubt that a court would entertain your request.  It is a very difficult time for all of you and emotions are running high.  Take a deep breath and a step back. You do not want to come across as the bad guy her but pursuing this may not make you look the best in your daughter's eyes.  Good luck.