I surely don't blame the family for insisting on a full investigation. Especially with the weirdness of the double hanging. From reading several of the forensic articles, it seems an astute medical examiner can determine the difference between an actual death by hanging and a death made to look like a hanging. It apparently has to do with internal tissue damage patterns.
It sounds like someone in the police department spoke about murder/suicide to a member of the press far sooner than they should have. Especially when the family members had not yet been notified.
Obviously the police have a whole lot more info than we have. Such as what they were wearing, evidence of activity within the house, etc. I thought I read that the real estate agent came to set up for an open house. In that case, the agent would go through the house turning on lights in every room, inside closets, etc.
I am kind of leaning towards the idea that the cops know what they are looking at. This is, after all, what they do for a living. But I also think a very thorough investigation should be conducted. I would want to know if the father had any rope fibers on his hands? And if it were my parents I would want to have a second, independent autopsy on both of them.