They ARE hiding a secret.. that their daughter is a lying, thieving, chronic sociopath. That their "princess" is a chronic criminal would shame any family. Especially one as self-righteous and "upright" as the As. Especially CA with her tone of moral superiority.
IMHO, the defense of KC is actually about the defense of the family image. To closed-system framilies, image is everything. CA and GA may feel that the fact the KC is a chronic criminal reflects on their child-raising.
BTW-- CA's note on her MySpace indicated that she thought KC was jealous BECAUSE Caylee was being put first, and too many of the family resources (and attention) were going to Caylee.
Many families go to enormous lengths to cover up secrets that are more prosaic-- like drug abuse, alcoholism, embezzing, delinquency, eating disorders, or spousal abuse. Because many families feel obligated to appear "perfect" or "respectable." Some wealthy families have sent their kids out of the country, when they have got into legal trouble, and then tried to rationalize it all away.
What does Caylee's paternity have to do with any of that?