Normally schools have a fixed number of EP hours a year, and the school gets to choose which child sees the EP.
There normally isn't a waiting list as such, in that the school and the EP would decide every term who the EP is going to see.
So, why on earth that child, who has been excluded so many times, is not top of the list I have no idea.
Normally schools prioritise kids with behaviour problems.
It's not legal for school to say kid can only attend 2 hours a day. Absolutely not legal - unless the parent agrees.
The parent needs to refuse to pick up kid, and send him there full time. Which will cause school more problems. Hopefully enough problems that they get him to see the EP.
Or, the school will have to send him home on a half day exclusion ery day. Then very quickly the child will have been excluded so much he'll be eligible for permanent exclusion. Then this will force the LEA to find him another school......
I can't remember all the law around exclusions, but once he's had so many exclusions she can also get the governors involved.
Has she formally complained to the governors about her DC not being seen by the EP? Or formally complained to the governors about the HT?
Even if the govs don't do anything she should still make a formal complaint.