She was already in an independent school who were doing very little, dancing around the subject and not tackling the issue at all. Class sizes were fairly large for an independent school and a variety of factors besides her schooling came into play. We moved house and schooling was a priority decision in that. Bit drastic granted but we'd have probably moved within a year or two anyway.
I don't think that independent school is the be all and end all. You need a school with a decent SEN provision or you will have to either buy outside expertise or do it yourselves. There are providers that do tutoring online. In school, she had group sessions twice a week for 30 mins and daily Lexia [10-15 mins] sessions on a tablet. The tips that the assessment folk gave us were acted upon. Simple stuff like giving her a handout with a question rather than writing it on a board. She'd spend 20 mins transcribing it from the board rather than answering the question. From time to time they worked with her with a scribe to see what difference it made to the volume of her output [massive] and worked with her for her Yr 6 exams so that she was focusing on technique - show evidence of verb, adverb, metaphor etc. So even if she could only write a short paragraph she was maximising her scores.
For me the assessment was the most valuable. How it presents in children can be very different and knowing that your child will struggle to memorise by rote spellings/time tables/a list of instructions [go upstairs, put on socks, find your shoes, get your coat and bag and meet me back here is far too much for example] but can expound for hours, study and become an expert in something that interests them is invaluable.
Re the two schools. Visit them both, see what grabs her. Talk to the staff, if school B are getting all the tricky kids are they getting funding and support. Bear in mind that kids who are bored and frustrated will act up. If they are progressing and engaged and being taught in a different way, "discipline" issues may disappear. Speak to school A, what's their action plan?
Get her assessed. It will be the best money you ever spend. Maybe get a recommendation from school B.