is it normal for the police to not tell a parent what they know?
Yes, and not just because the parent is a suspect. Police often give families NO information at all, even if an investigation goes on for years and it is clear that the family is not involved (e.g., the child was abducted or killed in a public place, the child is a teenager or adult and the parents are in another state, etc.).
Think of it this way: if you tell an ordinary secret--something that you want held in confidence--to another person, that person can inadvertently slip and reveal the information. So we are smart and we don't tell those things that we want to keep private. If the police tell parents "everything," then many, many things will leak out if the parents are overheard, slip up, etc. Not to mention that the suspects may be relatives, neighbors, friends, or others.
I'm not sure why people believe that parents are told everything by police. There are hundreds of cases in which parents have said publicly that LE doesn't tell them anything even though they aren't suspects. And if parents are told anything, they are likely told not to let on what they know. So there is no way that WE can tell, based on what parents SEEM to know or not know, whether parents are "suspects" or "guilty" or "know more than they are telling." We also can't know what LE will NEVER tell parents because it is unnecessarily cruel or gratuitous or because the information is crucial to identifying the perpetrator or because the evidence is crucial to a conviction. And we can't know what LE might be telling parents that isn't true and is designed to trip them up (see the Susan Smith case as a prime example).
I do think that a parent's general affect might say something if it is very "off"--but that, too, is dangerous. Better to try statement analysis to see what indicators there might be that the statements aren't true. And even statement analysis won't indicate guilt--just that a statement may be false and require follow-up questioning.
Usually when parents are guilty it is the story that is unbelievable. (The nanny took the child and the mother hasn't seen her for a month; a random black man carjacked me in the middle of nowhere and took the kids along for the ride even though no one saw it; the mom just got out of jail for cracking a baby's skull but the older child has been kidnapped...). Once a body is found there is a lot of forensic evidence that will sort things out quickly. There may well be some connection between the family and the killer, even if it is just a neighborhood one, but that doesn't mean that the family members are responsible for what happened. But at least in this case, we are likely to get a resolution.
