Im at my wits end with my daughter and I don't know what to do.

My 3 year old is horrible. I really don't know what to do. She hits me, kicks the dog, I caught her trying to push the cat down the stairs, shes mean to her older sister, shes just mean. I try everything, I can be kind and explain it, I can shout and scream, she just ignores everything I say. I sat her down on my lap today and explained that her behaviour was just not on and was making me and daddy sad when she acted that way. She farted and smiled at me and then carried on being horrible. I am just going crazy, I am constantly stressed and it was not like this at all with her older sister. I don't know what else I can try and I am ashamed and feel like a terrible mother. Often when it is just me and her during the day she is sweet and polite, but as soon as she has an audience of even her dad or sister she is a totally different child. She's very smart for her age, I know everyone says that and every kid is in their own way but you'd never believe she was 3 because she is so advanced. I've been working so much recently as we've just got a new cottage that is costing us a fortune, so I feel very guilty for that because I'm often giving her to her grandad for the day and she says she misses me and doesn't want me to go to work. It is her birthday tomorrow and I've spent all day today yelling and her and giving her time out (I feel terrible). It's effecting the whole family because every activity is ruined by her mean behaviour. Does anyone have any advice for me? Anything would be appreciated... I feel like I'm going to pop. via /r/Parenting http://bit.ly/2ESq7VQ