Here’s a great article by Mari Smith explaining the difference between Pages and Groups:  http://www.marismith.com/facebook-group-owners-need-know/

@alisonchandler-bird – I also like Groups just as  @amyhallbiz mentioned.  They are very friendly places because you get notifications when people post (either in an e-mail but people can turn that off, or at the notifications bar at the top of the page, or in a little number next to your Groups).  

But one thing I don’t like about them is you can’t advertise them, add apps, and they can get spammy.  I think if the Group is working well for you – sounds like a natural community of parents -then keep it.  You can add a Fan Page if you think that you need the branding but then you have the upkeep of both.  If you do add a fan page make sure you know the purpose of it.  
Facebook doesn’t take control of a Page you have started but they may classify it as a “Community Page”.