Moving out of state?

First of all, a grandparent has no standing (i.e. legal right ) to sue a parent for relocating out-of-sate; basically grandparents have no right to sue for anything for that matter.  The baby's father could sue but if your girlfriend establishes residency in her new state (it usually takes about 6 months), then she can file a custody case there.  However, her boyfriend could file in the original state first, in which case your girlfriend would have to return (and with the baby once its born).  If not, she could be charged with parental kidnapping.

However, until a court order is issues (in either state) she can move freely and legally.