So it came to a head in April when he was expelled from primary school. At that stage, he was living permanently with his mum but spending weekends with his Dad (and his dad was working some of those weekends)? When/how often did he see his grandad while things were 'normal'?
When he was expelled, what happened? Did his mum take time off work to homeschool, or did his dad (or you?) do that. Or did his grandad step in at that point? What happened over the summer holidays? Did he share childcare arrangements with your kids, or did his parents put something else in place for him? How does his Grandad look after him - does he feed him, buy him clothes, ferry him around to clubs, check he has the right stuff for school (uniform, books, kit), decorate his room how he likes it, etc?
I am wondering if he's essentially been left to his own devices since April, which will have an appalling effect on a child's mental health, especially if he's trying hard to deal with whatever it was that got him expelled. (Was he violent? Meltdowns? Persistent absence? Working way below expected level? Not all of that would result in expulsion but the general picture might help you and his dad work out what's going on.)
What's his dad gone since he was expelled? He's asked SS for help but not got anywhere. Has he been to the GP? Has he looked into what a private assessment might cost and how to go about it?
If child has been excluded since April, did he attend transition events for his secondary school? Did he settle in well or has he (again, it would feel like to him) been left to sort that out himself.
What's the situation like at your house? How many kids are there - who shares bedrooms with whom? Are there enough bathrooms for everyone who needs to to have a shower before work/school?