In Interstellar, why did NASA hold Coop away from his daughter when he first was brought into the NASA facility?

This would be standard protocol. NASA is a governmental organization. Its security would be handled by military personnel or civilian paramilitary employees. Coop no longer worked for NASA. He would not have been considered authorized personnel. He would have been handled like any other intruder. Even a current employee who was in an area or doing an activity they were not authorized to do would be held as a prisoner until cleared by someone with more authority than the security personnel.

The military has the 5 S’s of detaining prisoners. They are:

1. Secure - Relieve the subject of any weapons. Render them incapable of causing harm or damage. Ensure their inability to escape or be harmed by others.
2. Separate - Keeping the subjects from talking to each other keeps them from plotting anything or concocting/coordinating a story. It also psychologically subdues them.
3. Silence - Puts the subject on edge for future interrogation. Keeps them from influencing others around them. Keeps them from transmitting messages or codes.
4. Safeguard - Assume the subject has useful intel. This possibly makes the subject valuable. Treat them as such by providing them safety. Also, signatory countries of the Geneva Convention have agreed to treat prisoners in a custodial manner. In other words, ensure the safety, health, and wellbeing of the prisoner. This includes providing sustenance, shelter, medical care, and personal protective equipment.
5. Speed - Transport the subject to personnel or facilities of higher authority for further detention or interrogation as quickly as possible.

Two unknown people show up at a secret government facility in the middle of the night.

I think it seems quite reasonable that the security of the site (which may have been entirely robotic) would detain and separate the intruders, until they can ascertain what threat they are and what to do with them. Separating them seems reasonable from the point of view that talking to them individually may reveal more and people are less of a threat when they can't cooperate as a team.

It's not clear exactly what time of the night this happens, but it's not early. Its after dark and it is summer time (they are growing crops).

It's entirely possible that the senior staff were off-duty at the time. It may have taken some minutes to ascertain that Cooper was who he said he was, and decide that it was worth introducing him to the senior NASA team.

Coop is an adult, while her daughter is below 13. Because they have broken in to the facility, it's the adult who needs to be interrogated and not the child. This is the reason they kept Coop into the room, while the daughter was taken care of by Dr. Brand's daughter.