Strangling as a way to kill someone sounds very personal, not something random burglars would do. If they wanted to silence Caroline they could have stuffed a t-shirt in her mouth, threatened to kill her child if she spoke, or even beaten her - all of it simpler and quicker than what they did. Strangling a person is brutal: the victim tries to defend herself, hitting and scratching you, it requires strength and it's not at all quick. Caroline might have taken several minutes to die. And why not kill the husband, too? Why just tie him up?
Of course, it might've really been a burglary gone wrong, but I wouldn't be surprised if the perpetrators knew the family. Also, the fact the police considers the husband's psychologist's statement "crucial information" is so odd. He isn't a suspect, but maybe he had enemies that might have wanted to hurt him?