Can a kid in foster care go across state lines?

Yes, but it requires a court order authorizing the travel; it's up to the case worker and judge to allow it or not.

The foster parent's for the children that I'm adopting have taken many of their foster kids on vacations: especially on cruises (even ones that visit foreign countries). According to them, it's important to have the case worker to be aware of your travel and ready to answer the phone if needed, and you'll need a stack of paperwork to be able to prove that beyond a shadow of a doubt that you are the legal guardian of those children.