As to how the parents would be expected to react on finding that they were the suspects- well, of course, they'd be upset whether they were guilty or not. That question really doesn't add much to the investigation. If they were innocent, they'd be upset and horrified. If they were guilty they'd be upset that whatever they were trying to portray wasn't working.
Either way, the relationship between the family and LE was bound to become adversarial as soon as defense lawyers were hired and the body was found in the home.
As far as Hunter driving the investigation- not sure if it is the same in every district, but here, if the parents wouldn't go willingly to the station (they were under no obligation to do this, and by that time they already had lawyers who may have told them not to go) then an arrest warrant is needed and the DA issues that. If that hadn't been the case, the BPD would have arrested them. But they still wouldn't have to talk to police. But I'd think if they were innocent they'd want to, even if they felt police thought they were guilty. I'd be doing everything I could to change their minds.
Whenever parents of a murdered (or missing) child won't talk to police, it would be viewed as suspicious behavior. When such interviews have to be brokered by defense attorneys, it seems suspicious as well. The R lawyers were hired to keep them out of jail- this by the Rs admission as well as the lawyers. That's what defense lawyers do- they really don't care about solving the crime, they don't care WHO gets found guilty as long as it isn't their clients. Not just this case, ANY case. And in cases where the client's guilt is obvious, they'll plea bargain or try an insanity defense.