Sounds quite similar situation to mine although I've only 2 children, both girls.
Your daughter may or may not have asd / adhd but she does sound so much like my 10yo, who is diagnosed asd. I find that very little demands on them at this age works best, as long as you set clear lines that cannot be crossed.
Also puberty hormones, transition to secondary, friendships issues etc all contribute for difficult emotions but her being physically abusive towards you is not acceptable. You need to really come down with a ton of bricks on that one. Explain calmly that you will not tolerate physical violence and if it happens again then xyz will happen, (whatever you feel is an appropriate consequence but mean it and stick to it).
Think of things that absolutely must get done such as school work, personal care and set bedtimes (my dd never slept until gone midnight for years, she's now taking melatonin which has saved my sanity and improved her mood as no longer physically exhausted).
When she screams & shouts etc try to remain calm and say you'll discuss when she's calmed down or similar (lord knows it's easier said than done but really does help not to rise to the behaviour). Staying calm and non judgmental helps, demonstrate the behaviours that you'd like her to learn, you are the role model and it takes a LOT of practice. (I still lose my shit occasionally but 90% of the time I do not retaliate and just acknowledge her feelings, even when she's screaming she hates me).
Your 5yo sounds like they could be copying what they see behaviour wise, I had this with my younger daughter but now she's 7 it has almost stopped.
Speak to school to see how she is there, ask to see the senco too as they may be able to signpost you for more support for your dd.
I'm sorry it's long and may sound preachy, but I really do know how challenging and exhausting parenting children with difficult behaviours is. I have no family who are healthy or young enough to offer support, husband is a workaholic so all lands on me.
I work 3 days and as stressful as it is, I do find it helps to stimulate my mind and it's nice to have calm adult conversations.
Lastly remember that you are the safe person your kids can express their emotions with so unfortunately makes us emotional punchbags. Do try to address the physical side of things though as I feel if it continues it could spiral and at 11 she should be able to control her lashing out.
You sound like a lovely mum who is doing the best you can by your children. You are not alone, it's sometimes really hard being a mum.
