He obviously does have SN in the broader sense: his needs aren't typical, he's needed professional input, and 'normal' step-parenting methods aren't working. But neither of his biological parents, nor his biological grandma want to discuss or consider any oddities: again, very common. And you're going insane with the frustration and worrying that his sibling is suffering... also very frequent.
Not all SN are 'diagnosable', and some are even the direct result of anxieties, family traumas etc. Even for the diagnosable type, a label for the problem is only useful if used as a pointer towards appropriate help (and most of the time it's only parents who do anything useful anyway).
So if, for the moment, we assumed that he a) has an ASD and b) would be correctly diagnosed by CAMHS, who would benefit from the diagnosis.
You would, as you want to know how to help him better, and whether it's a good idea to accommodate his eccentricities
Your DD might, as you could explain 'why' her DSB is how he is
His mum, dad and grandma wouldn't, as they're quite happy with the status quo
Your DSS would be helped a bit by your increased knowledge and understanding, but hindered by the misunderstandings and hushed voices talking about whether or not he's 'normal' before it erupts into an almighty row in which you're the chief villain, aided and abetted by 'those doctors who don't know what they're on about, nothing wrong with him'. The school would carry on as they are at the moment, because not much is offered by schools unless they feel like it (and regardless of whether or not a dc has a particular diagnosis). And your DD would be piggy in the middle.
And if he doesn't have asd (or if he does, but never gets assessed so it's unofficial forever), you can still accept that he has some autistic-type quirks which needs special handling, and you can give consistency by copying his mum's house. Cos she definitely isn't going to copy yours, no matter how much better you feel your home's routines are for your DSS
Practically speaking, I wonder if the long-term solution is to approach cafcass and/or your DD's dad with the situation, and see if your custody /access arrangements can be modified to allow her to have more time without her DSB.