The same principles as we discussed apply.
I do not know why a SC CPS agency would be pursuing a matter for a child that resides in NC (this is likely something that is very fact specific that you are going to want to discuss with your local attorney when they get back in the office after the holiday weekend).
But you still have the same rights - CPS has no independent authority to enter your home, you cannot be forced to incriminate yourself (so you do not have to speak to them without your attorney present - I do not recommend speaking to these individuals without your attorney as things that may seem innocuous can easily be misconstrued or taken out of context).
A law enforcement officer can obtain a warrant (this requires a judge signing an order) to enter your home, and they can also obtain a warrant to recover a child.
Both of these require the officer to make a showing of what is called "probable cause" to the judge (so the officer must present an affidavit (a sworn statement) detailing why they believe either the search warrant or the removal of the child is required prior to any hearing). This is a very high standard (so first the CPS worker must convince a police officer, then a police officer must convince a judge).
The child is already vacationing over a holiday weekend. (This isn't like you were under fear of a CPS investigation and shuttled the kid off). Not that you couldn't do this (this is legal, it just makes for something that your attorney has to deal with in future proceedings - it is a perception issue).