Which county you in?
The school isn't working and once this is resolved she will be an easier child. Is your other children in this school too? Is it possible to look at another school in the town? Some schools are more accepting to sen and also more inclusive. Does she like her school teacher?. Also does she have someone to hang out with? Have you tried to talk about her school day? Look at her timetable and pick out which lessons she likes and hates. Try to find a pattern etc.
Until something is changed with the school / could be the teacher / or the friends it will be hard for her. Is it a massive school with lots of children or a small school due to sensory issues / noise (tell the teacher she wants to take in fidget toys etc). Does she find the work too hard? (dyslexic) or hard to concentrate (adhd)
Also, social services - it would depend on which county you live as some will look at a child in need and some will assess as a child with disabilities. (CWD is the correct way however in some LA Pda comes under a CIN)
Unfortunately, I think if possible it might be worth going private to get your reports / diagnosis (yes you should be able to do it under the nhs but you could be waiting a long time). Equally is there an outsource ASD school locally to you that will come in and watch your child at school? (they can see things which a general teacher cant see) ask the senco. An EP might able to spot the issues if she good / your daughter would cooperate with the tests.
Teachers are not your friends - you could be in a battle with them later down the line. Even the most experienced teachers 20 years plus can not pick up on asd/ pda - my kid was under the rador for years. Make sure you write everything down as if it comes to EBSA (emotionally based school avoidance) / fines then you need your evidence (which is all wrote down / email to teachers etc).
Have you tried to have a meeting with the senco? some are rubbish hopefully you have a good one at the school. However id advise meeting with them (but put the request in via email) and along with your teacher (everything needs to be wrote / emailed) and highlight your child's struggles (this is your evidence for later down the line - even you might use this evidence as "mum reported this issue via email on date / year"
You prob will need an EHCP (you can apply for one of those today using the IPSEA website if in the UK)
Have you seen the PANDA diagram on the pda website? hopefully this diagram has linked the right thing https://tse3.mm.bing.net/th/id/OIP.8EMGlHbptobhk3F1qXmaRwHaFj?rs=1&pid=ImgDetMain&o=7&rm=3
I would ignore anyone who hasn't had experience with a SEN child / especially a pda child its absolutely exhausting and until you have seen it first hand I wouldn't take any advise from non sen mums or advise on how to "manage a child"
If you have any grandparents that can help out use them.
Keep dividing the family so everyone has some nice times and some special times even if its playing a board game with the other siblings.
Any spare cash get a cleaner in.
There are some good facebook groups to get knowledge. Which county you in?
Good luck, keep going your kid is finding it the hardest here until something changes at school. Try to reason with her and negotiate that will help - treat her like your friend - same level which is weird (not mum / daughter relationship).
Keep going mummy you got this! nearly easter and the kids holiday and no school :-) hopefully you can just chill. Divide and conquer so the other children have a bit of nice time with you.
Also, try and talk to the child if she can articulate what she is finding hard but its might be too hard for her to explain. Make it simple. Try and have a bit of a diary for yourself to see if you can spot any trigger points. We found a pen and paper the easiest way to communicate
You are doing a fab job - keep going - its so hard. Hope the weekend is a chilled one for you all