The police can question children without parental permission. Children can be questioned about something they may have witnessed or their involvement in criminal activity. However, no one, neither adults nor children, can be forced to speak with the police. Just as adults can decline to speak with police, so can children. And if a child requests a parent, lawyer, or other adult present during questioning, the police must respect that and terminate the questioning.
If a child was questioned by the police, without any other adults present, certainly the issue of coercion or duress must be closely examined. Additionally, if the child was in police custody and interrogated by the police, then a Miranda warning is required or else any statements the child gave must be suppressed and ruled inadmissible at trial in a criminal matter.
An unfortunate example of this situation is Brendan Dassey from the series “Making a Murderer.” Statements he made as a teenager to investigators while being interrogated were used to convict and sentence him to prison. His conviction was recently overturned on appeal, however. More information about Brendan’s case can be found here: https://www.facebook.com/brandtdefense/posts/1084914624895102.
We hope your kids are never put in any of these situations. But if they are, you and your kids should know your rights and options.