I think that when KC first had the baby, CA pitched in an basically did all the things any grandmother would do when having a precious little granddaughter in the house. KC just sort of sat back and let her mom do all the things a mother does. She took great advantage of the fact that she and Caylee lived with CA and GA. Over a period of time, CA and KC probably had many conversations and arguments about how KC is the mother and it's not right that CA, as the grandmother, has to raise another child. KC just went about her life, playing "momma" for photo ops and when others were around, but I guarantee you that when they were in that house, KC sat back and CA had to be the mother to Caylee.
So, in the recent past, CA probably told her daughter that she has to stop the partying, put the baby first because this is what Parents do! When you have a child, your life is no longer your own! CA had a job, had other obligations, and it must have galled her to see her daughter thumbing her nose at her responsibilities when it came to the baby.
Casey grew resentful as CA insisted she must be the one the parent the child. Being so full of herself, she would reason that her parents didn't have anything to do anyway, they were just being ridiculous and were intentionally making it hard on her.
This scenario goes on in thousands of homes. Adult child has a child and pretty much depends on grandparents to do all the parenting. They take advantage and when the grandparents finally get tired of doing it all, trouble ensues because the bio parent believes they are being "mistreated" by their parents. They think their parents are being unsupportive because they feel entitled and think there is nothing wrong with their parents raising another generation. How dare they!
"Fine, you know what? I am doing the best I can! I have to work nights, I have to earn a living! You don't want to take care of Caylee anymore? Then we'll just get out of your lives and you'll never see us again!"
Most of the time it doesn't end up the way this case has but if the adult child happens to be a sociopath, bad things can happen to the innocent child.