Please help. 3 year old behavior

I don't know how to parent my child anymore she's 3 and half and has not always behaved this way. I don't know which direction to go and all we do is scream as loud as we can and has stern as possible because it's the only thing to startle her enough because gentle parenting didn't work, because sending her to her room and telling her we are here for her didn't work. Because teaching her the right way and showing respect didn't work. I feel like dying, I feel I have failed her. When she's angry she spits and hits. Or she will spit everywhere despite us telling her for a year that if she spits she needs to spit in the toilet. She hugs the dogs so hard she almost chokes them clear to death. We teach her everyday pet with an open hand and she will start doing that and grt out of control and hug them as hard as possible. She will chase them endlessly and back them into corners. The more agitated the dogs get the harder she laughs. We will put them away in there cages and she will go let them out of the cages. We tell her not to go near the cages and she does so smiling. She's incredibly intelligent, you can have an adult conversation with her. She can say and understand very large words, she can tell you the directions to the grocery store and people's houses. I worked hard for her 3 and half years of life trying to raise a calm sweet and well behaved child and I'm tired and she's mean she will literally tell us to "leave her alone" and " don't talk to me" . I'm sad, I'm tired and I'm defeated.