sounds like you are having a pretty rough time with your daughter

something i was taught in psychology when training to be a Nanny is ....punishment is reward.... by getting a child to bite on soap or partake in any other form of punishment you are giving them attention, even if it is for the second you are instructing them. the rule for disencouraging bad behaviour is to withdraw all attention till the episode of bad behaviour is over at which point you reward for the good behaviour they are now displaying

have you tried totally ignoring her and concentrating on getting everyone else to leave the room when she kicks off telling them loud enough for your daughter to hear that you are all going to somewhere that is calmer because you do not like the..(specific behaviour)... that (your daughter) is doing, rather than sending her to be alone, the result is the same, no positive reinforcement of her behaviour or attention being given to her, but the reaction may well be different because you are not giving her any instructions to rebell against. do not direct the conversation towards your daughter even if you are alone in the room with her when she starts, just say a thought out loud e.g i think i should go into the... because i do not like the .... that (your daughters name) is ..., always say you do not like the specific behaviour so she will begin to piece together the bits you do not like rather than think it is all of her you don't like. if you get a few minutes of calm time, try telling her you love her as a person but hate her behaviour when she ....(the specific things you don't like)..... that way again she will begin to realise her behaviour is not the whole of her and it will become easier for her to try and change it.
try making a specific area of a room away from the 'public' areas (not her bedroom, she will by now associate this as a place she goes when being punnished) into a place she can take herself when her emotions are becoming overwhelming, (involve her in making it, deciding where to place it and the acceptible behaviours in it... throwing against a specific wall, punching or biting softies are acceptible throwing softies out of the area is not. she may wish to decorate the area with stickers or a target to throos things towards, this is ok, anything to make it her own safe place where she is happy to go to.do not insist she goes there, though you could gently ask if she wants to when you notice the start of an episode) make it safe with lots of soft cushions and cuddly toys that she can throw or bite or punch if she feels the need to (let her choose them as specific toys for her to take her anger out on that way she is more likely to use them for that purpose). let her know that it is ok for her to go there and express her anger/resentment when she feels the need to, reassure her that she will not be disturbed whilst she is in there and praise her for using it when the episode is over. this will let her know you are trying to help her to deal with her anger/emotins, that you acknowledge they are things which are a part of her, and it lets her know they are not acceptible around others but do need addressing and working through. do not get cross if any of the softies get ruined, ruined softies are better than ruined treasures! your daughter may get very attached to certain softies so please always ask her permission during a calm time before washing or disposing of any of the softies and explain to your other children these are just for your daughter, they need to respect them like they should respect your treasures.
do not force appologies, your daughter can not be responsible for behaviours she can not control,
over do the praise for any attempts to change bad to good behaviour, if this is rebelled against, next time try a smile and nod of the head to acknowledge you have noticed it without the niceties which may be uncomfortable or embarrassing to your daughter.

please do not bribe with treats, it never works long term and the bribes expected become larger and more expensive over time resulting in a spoilt brat who manipulates her behaviour depending on the want of the bribe

http://en.wikipedia.org/wiki/Oppositional_defiant_disorder

hope this helps