My son. Ds1 is twice exceptional/ dual exceptional / 2E / DME (why can we never have just one name for something??!!!).
For a while at primary school, he was doing well and then he started to fall behind as his learning disability started to have increasing impact. However, he was still making slightly above average progress and that meant the school didn't care. The SEmCO told me that he'd have to be a couple of years behind the minimum before they would take action.
I got a private report done and now there was an official diagnosis of his SEN as well as an objective measure (or series of measures) of his intelligence. I was also advised that under the Disability Discrimination Act, the school would be acting illegally if they refused to acknowledge the learning disability.
So, I delivered the report to the school and presented it in writing, not at a verbal meeting where there could be later confusion about what was said. I got a letter back acknowledging the diagnosis but telling me that the "good news" was that DS didn't qualify for inclusion on the SEN register because he wasn't far behind enough.
Verbally the SENCO said to me about DS's SEN. "Oh, they have a name for everything these days." He has dysgraphia, which is in the dyslexia family. It has been recognised for decades -it was named in the 1940s.
The upshot was that the primary school were beyond useless. However, at elast the diagnosis (or was it my fire breathing dragon act?) stopped the SEN from calling DS lazy after that.
When he went to secondary school, I was very nervous that we'd get more of the same. The (feeder) primary school had failed to let the secondary know about DS when giving details of all the other pupil's SENs. However, the secondary school want the students to do well and so they were interested to find out about it and wanted to know as much as I could tell them. Then they came up with a plan for DS to help him prevent his SEN from getting in the way of reaching his potential.
Its early days yet, but he's back in the top set for all the academic stuff, and for the moment things are going well. The dysgraphia is still dragging his work down a little but DS is learning to cope with it and the extra time in exams gives him a fighting chance of being able to get down most of what he knows.
Regarding schools, what i have learned is that if they have made up their minds not to help, then you've lost before you start. however, if you can find a school that is willing to help, then together you can make a difference.
Sorry its so long. I hope it helps a little.