I don't think Killer's family believes one single aspect of any of her stories. They know her well enough that they can't possibly believe anything she says. They want money donated to her "cause" and they know that most people are not going to donate funds to appeal a murder conviction unless they believe the person to be wrongfully convicted. So, her people try to convince as many as possible that Jodi is a victim.
Their being total insensitive jerks toward the Alexanders is unexplainable, though. How does one justify something so beyond reason? Mentally ill people do stuff like that; are we to assume the whole family is mentally ill? I don't mean crazy...I mean a real, actual mental illness. Could they all suffer from one? I doubt it, to be honest. I think they are not ill at all but just plain crazy, but mostly greedy. The monetary gain they have received might continue for some time before it diminishes and finally ends. When that happens, they will become noticeably less vocal.
JMO