This is what I always thought happened:
While I believe that ICA and CA had a turbulent relationship, I don't think that ICA intended to murder Caylee. I think after the big fight, she left the house in a big snot with Caylee the way any overindulged, stroppy teenager behaves when they are told "no". After leaving in a huff, where was she to go? Tony liked her like a teenage boy- flat on her back, and was not looking for a wife, much less a wife with a baby daughter. ICA wanted to get away from anyone she ever had to "answer to" in her life, and just be free to be a party girl, especially this night when she wanted to shake off the memories of the fight with CA.
She couldn't drag Caylee into her boyfriend's place because that would ruin the sex & party vibe, so like usual (I believe) she gave Caylee xanax (zanny as slang) to knocker her out for a few hours, so she and Tony could get down to business. Except when she eventually went back to the trunk of her car, she realised she gave Caylee too much and she had died.
Now being selfish and stupid the way only an immature, selfish, spoiled brat who has never had any personal responsibility can be (after all, CA & GA mainly looked after Caylee, while ICA faffed around free as a bird all day pretending to work), and because her family is so dysfunctional and has believed all her lies for so long because it's better to live in denial and think your family is perfect than really see what is going on (a pregnant teenager who dropped out of high school, a husband secretly more interested in escorts than his wife, a wife who is a control freak and an emotional abuser, and a son who wants nothing to do with his family).... of COURSE she thinks she is so sneaky and smart that she can use her wits to get herself out of the mess she created.
She drives around with the dead body of her baby in the trunk, decomposing in the heat of the Florida sunshine for a few days while she tries to come up with a plan. Eventually, she decides that the only way she will look blameless is to say that Caylee was kidnapped. Everybody feels sorry for the mother of a kidnapped, really pretty baby, right? Her parents will buy it because they've always bought her lies. And because of that, she assumes that she must be pretty smart and far ahead of the entire world, because it's never done her wrong so far in her life: stealing from Grandma, telling her parents she couldn't possibly be pregnant because like Mary, she too was going to have a virgin birth. If they believed all of THAT, why wouldn't they believe her kidnapping story?
So she comes home for gas cans as an excuse to get the duct tape. Dammit, Daddy- stay away from the car! Don't all kidnappers blindfold and cover the mouths of their victims? Gee, all the cop shows & movies she has ever seen have something like that in then, right? That will make it really authentic! People will feel so extra-sorry for her, the poor, poor mother of a kidnapped baby- never in a million years will she be blamed! Maybe Caylee being dead is really a blessing in disguise after all, she thinks. Now she can have the Bella Vita she has always wanted, and she'll move out on her own, and with Caylee gone she can just cut ties with CA for good- there will be no reason now she'll ever have to stay in touch or be under her thumb! The only thing CA was ever good for was watching "the brat" when she wanted to go meet guys and party.
Except getting rid of the body proves harder than she thought. When can she do it? Where will she put it? Could she trust anyone else with her little secret to get a bit of help? She dumps the body in a familiar location with no other thought than she knows for certain that nobody really ever goes in there so it should be a relatively safe graveyard. Then she decides that maybe she'll say that the kidnapping happened when her car ran out of gas like it was prone to do, when she accepted help from a stranger. Or maybe the kidnapping was a carjacking and the carjacker took off with Caylee in the backseat. Then she could just dump the car at Amscot and feign ignorance.
Except the plan went wrong when CA finally caught up with her and dragged her home. She wasn't counting on a face-to-face confrontation again, and because she was also a bit scared because this was such a huge almighty lie, she couldn't get the words out. By the time the police got involved, she regained some of her liar confidence, but chickened out of using the story she originally concocted for whatever reason. Maybe she was slightly intimidated by the police involvement. So she kept some of the details the same as she was put on the spot- the kidnapping, and then the name Zanny which just came off the tip of her tongue. Then it all snowballed from there.
Either way, I hope she sizzles in that chair. And I hope CA and GA aren't too far behind her for all the lying and trying to circumvent justice for their innocent granddaughter. They deserve to be punished for aiding and abetting a murderer.