ZD,
“And you have to go to an a beaurocrat who thinks religous schools are nonsense and when they refuse you have to convince a arbritor that private schools are better than public schools and again many of them do not belive in relgious schools and certainly do not believe in segregated schools (in the relgious sense)”
The special education that is provided in separate schools for the most part are for children with severe disabilities. Including leaning, physical and emotional disabilities. I have dealt with a good number of excellent special education schools/programs run by orthodox Jews. A number run by chasidim. Not one of them was a segregated school. They all services both boys and girls. I have never seen a segregated program. The school in KJ service both Genders, I know several schools in Boro Park and Williamsburg that are run by Chasidim with beards and peyos and their schools have both boys and girls in the classes.
Your assumption that the reason why Jewish Parents want other options than the public schools for their children is because they want gender segregation is a specious assumption without any basis in fact or reality.