Obviously at the time of this phone message, the family believed Caylee was alive and with someone, or were hoping very hard that she was. (According to all the people interviewed) KC had been a loving and protective mother all of KC's life, the family and close friends had absolutely no reason to believe that KC had harmed Caylee. They thought Caylee must be with someone who knew Casey, whether a friend, or someone with a vendetta against KC, someone she had stolen from or who knows what, or a sitter who had gotten too attached or whatever. Finding Caylee took priority over trying to figure out what was wrong with KC, certainly they would never have thought of going out searching for a dead body. What family could do that when they were still thinking the child was alive out there?
I think they (especially Lee) did all the searching they could. They couldn't go bang people's doors down for information or to search for Caylee, as Lee said. They were dependant on LE, they could only pass all info on to LE.
They were the ones who called LE. They cooperated fully with LE despite the fact that some of LE repeatedly indicated they believed KC had killed Caylee and their actions (at least on the part of one or two of them) repeatedly showed they were only concerned with building a case against KC. How many families could handle that, imagine the fear of the family thinking Caylee was still out there but how could they find her on their own, etc? What about LE taking search dogs to the places Caylee and KC had been for example, to start with?
(If you were the grandmother of this child you wouldn't have been telling the police about this picture and wanting them to find out whose apartment it really was, etc? You wouldn't have wanted them to find out everything about everyone who had been in contact with Caylee, and everyplace that she'd been? I sure would.) LE told all witnesses including the family to contact them if they thought of anything. That's what CA was doing in this phone messg.