Well, lets look at it from their point of view - the last time Cw's father saw him was before his arrest, when Chris told his father 'what had happened'. His father believed him. The next thing his parents know, Chris is going to plead guilty to ALL murders. They are not allowed to discuss this with him, so they can't test their understanding. They have no information at all, whereas I believe that Shan'anns family do know a little more.
I think Chris's parents are desperate for information. When this is available to them, I would hope it makes things clearer for them. I am surprised that the PD team hasn't counselled them as to the reasoning behind the plea, but perhaps they have good reason not to.