I think there is some significance to June 9th also. I wondered if Casey did move out that day, without Caylee, while planning on moving in together with Amy. She could have left Caylee with Cindy and a week later, Cindy finally told her to basically chit or get off the pot, start being a mother instead of the party girl.
I also think the family wasn't fond of Casey's new boyfriend, not because he is a bad person, but possibly because Casey started putting Caylee last since he was such an important part of the club scene that she wanted to be in. Fame and all, ya know. *sarcasm inserted here*
But what I think everyone is stepping around is June 15/16. I am almost certain there was an argument, as stated by the neighbor, between Cindy and Casey. Something happened at the Anthony's house that day to Caylee after Cindy and George went to work, IMO. Casey didn't take Caylee's favorite teddy bear or her toys and clothes because there was no Caylee. From that day on, Casey made excuse after excuse for why Cindy couldn't see Caylee.