In the hope that it will make you feel better, I have a teenage daughter who is absolutely lovely now - kind, generous, hard-working etc. BUT she was utterly vile as a toddler! She had temper tantrums lasting 2 hours, was violent - regularly bit other children at nursery, and when we finally got it through to her that she couldn't bite, she went through phases of hitting, nipping, pushing etc.
What worked for me were:
a) working full-time - so only had to deal with her weekends and school holidays (I'm a teacher)
b) Pick your battles, and once you have picked them be consistent eg. I never tolerated any kind of violence, but the juice thing wouldn't bother me - I'd just water it down as though it was squash, and only allow it once a day.
c) Lots of active stuff: walks out, days out, trips to the play park, swimming etc. She loved going for long walks in the push chair, so I'd choose a playpark a good hour from home, walk there, let her play for as long as she wants (it was good for her and tired her out), then walk back
d) when in the house, lots of attention - she loved books and crafting activities, so DH and I took it in turns to read to her, bake with her, painting etc.
e) when you know that saying 'no' is going to cause a 2 hour temper tantrum, DO NOT CAVE in - just accept it, accept the screaming, it's not hurting them. I can remember being out for a walk with my DD and she decided she didn't want to sit in the push chair, she wanted to be carried - I couldn't physically carry her AND push an empty pushchair, so her choice was either walk, or go in push chair. Cue 2 hour temper tantrum on the path, while I had to just there and wait for it to pass (I wasn't caving in!)
It only got better once she started school, but she was about 6 before the tantrums pretty much stopped.
She still does lose her temper on very rare occasions, but the punishment is loss of phone and all electronics and in every other respect she's lovely now. Still very active though - sports, drama, art, music, she gets involved with all sorts of things, and does stuff most nights after school.