I'm going to summarise what I think the Op is trying to get across and from his other posts to. Clearly there is a lot going on here:
-OPs ex was concerned about sons behaviour and took him to a doctor for an assessment. This was done in part online and then an hours assessment by an assessor with the son
-OPs ex told OP he had been diagnosed.
-OP looked at the detail behind it and contacted the doctor who says it was not a formal diagnosis but an opinion.
-At the time of diagnosis the son was experiencing a traumatic time and refusing school. He rang OP and police several times reporting his mum for punching/kicking and slapping him.
-OPs ex reported him for abuse and was granted nonmol order so the Op did not see the son or other child for 9 months.
-During this 9 month period the school were concerned about sons appearance as he was often unwashed, unclean, lacking a haircut and other concerns about his appearance. They reported this to social services who got involved
-OP took evidence to the courts proving the allegations against him were false and he was granted access to children again and now has them half the week
-OP found out other things that concerned him: grandma threatening to record son naked, son being allowed to vape at home and that he was allowed to be awake all night.
-Behaviour seemingly improved with contact with dad again
-Latest is that the ex has now told her son that he has this diagnosis. NHs consider the private appt as final and wont reassess but school and Op disagree
All of the above could be down to either a struggling boy with autism or a struggling boy who's parents are at odds
OP, as has been said a MILLION times on this thread, take him for a private appointment yourself to be assessed if you doubt it. If you have parental responsibility then there's no reason you need to get his mums approval.