johnnyd - so sad to hear what you and your family have been through. i haven't been there, but understand your frustrations. being a parent of a 4 years old can be so so hard and being a 4 year old can be really hard too . all i can do is offer some things that my ds's teacher told me which have helped me with my 4 year old ds:
1.your children hold up a mirror to your own behaviour
2. this means you have to be the best role model you can be in order for them to manage their emotions (you can't be 100% all the time, but i found when i began to consciously react/respond differently to his emotions or events ie.spilling food on the floor, being late for something dramatically changed things for the better.
3.a detailed example would be tidy up time - instead of threats or demands try 'xyz could you help me put these toys away?' 'no!', 'well we need to put them back in the basket so they don't get broken or in case you step on them and hurt yourself, lets keep your toys and toes safe, then we can read a story, make popcorn etc' - make it into a joke and try and keep your tone of voice level for the request.
4.prepare yourself as much as you can for the next day the night before, hopefully taking away further opportunities for stress or being overwhelmed, being late, trying to do to much in too little time.
5.prepare your daughter as much as you can for each day the night before, let her know whats happening, where you are going, what to expect, who will be there, what she will wear etc., on the day, give her lots of warning if she is in the middle of something, be a few steps ahead, if you need to be out in 1/2 hour don't put on a hour long video on. 'after breakfast we are going to the shops and then the park'. then after breakfast say 'ok time to get your shoes on' give her a 5 minute window to find them and do it so she has plenty of time. lots of praise when she achieves this
6. the key to turning things around is to focus on what they CAN DO rather than what they can't. another example would be if xyz keeps spilling her juice - instead of saying 'don't spill your drink' tell her to 'hold on with both hands xyz, thats right, thats the way' lots of positive reinforcement.
7.structure your day, i tend to do active stuff in the am, and then come home for lunch and let them play in garden, puzzles, playdoh, water play, video in pm. danger time use to be between 4 - 6 pm, trying to make tea when both ds's hungry and tired. try and anticipate by letting them help or video, or baths seem to be the best relaxation for them. i also second freckles advice re: cranial osteopathy -go for one that specialises with children and by recommendation. there is a brilliant one in devon if you are nearby.
8.another thing that may help is if you can't avoid the tantrum/conflict is to really help her through it. give the emotion a name: 'oh xyz, i can see that you are really frustrated that abc has taken your doll' you could try and offer a solution 'you could let abc have a turn you can play with this doll' etc. the more times you talk about emotions and what they are called and what they feel like the more your daughter will understand her feelings and be able to articulate them rather than act them.talk about it afterwards when you are both calm without judgement, reassure her that everythings ok and you are so happy that she is now calm and quiet.
9.get rest, can you let them stay at grandparents or ask your dh to take them camping for a couple of days/ take them on a long train ride/swimming etc.
she is probably striving for her independence and also wants to copy mummy - take it as a compliment and see it for what it is that way you can distance yourself from your emotions.
if interested you could look at non violent communication and look under parenting articles, they believe that all children are inherently good - they are just trying to make sense of the world
best of luck and begin to think of this as a wonderful opportunity to turn things around and try and ask for some rest