Lets clarify this..
It is 'One Party to the conversation'. Not 1 person. This means you have to be party to the conversation as opposed to just knowing about the taping. This is a very important difference as it means that a CP can not tape the conversation between the child and the NCP. The CP knows about the taping, but is not party to the conversation. So, it would be illegal. The moment the CP takes the phone and becomes a party, then she can tape legally.
Also, it is not 'Two Party' it is 'All Parties'. Therefore in All Party states, everyone taking part in the conversation needs to be aware, not just 2 people.