KC tends to blow up and attack when she is "frushtrated" - something we have seen for ourselves in early visits, and heard from Tracy M's depo, when she snarks back to her dad to stop being a cop and start being a dad, simply because he confronts her and demands an explanation. We also saw the petty statement she made JB read regarding how her wishes had not been met by the family regarding Caylee's remains.
I think she continuously uses others to lash out at or as scapegoats when she is not the center of the universe or they are not fulfilling her wishes. It's not pretty and the family I'm sure realizes she does not know how to act appropriately at any given time. To spare themselves the embarrassment and to avoid giving her another chance to show how insensitive she is to anyone but herself, I think they have stayed away.
She has also managed to refuse visits to them in the past out of anger. I can't imagine that, given how she barely acknowledges them in court, she has not built up a huge wall of resentment that they have not managed to make this all go away for her, and that her attitude would spill over into a visit unless it was so carefully choreographed that everyone was reading from a script.
I can see any one of them telling her they love her and KC launching into an angry tirade of why that just isn't true. The unspoken reason they all don't want the visits recorded is the fact that they could get very ugly, I'd imagine.