Leave dd where she is- she's got a scholarship. Say to ds- sorry, that school was only a possibility if you got a scholarship and sadly you didn't, so you will be going to X school in September.
This!
Don't move DD!
YY to all the people who've said to treat them as individuals, and that's it's OK to send them to different schools.
It's not as if you're financing DD's private education, and refusing to give the same opportunity to DC2/3, anyway, is it? She only goes there because you didn't have to pay for it in the first place.
She has got there on her merits, end of! Whereas I can understand everyone's disappointment that DS isn't able to go, if it were my family, when we got the news that DS hadn't made the grade, that would have been the end of it.
You need to move on. I can understand your DH's weariness tbh, if this is a case of him saying "We can't afford to send DS" and you saying "Yes we can, if we move/take DD out of her school/if I can only get another job" etc, etc.
Has DS been under the impression that he might be able to go to that school even if he didn't get a scholarship? It should have been made very clear to him that the only way he could ever go, would be if he won a scholarship like his Dsis.
Can I just point out that if you move your DD, who is a music scholar, I imagine that the music provision will be nowhere near as good in a state school as it is at her current school.
IMO you are being VVU to consider anything other than your DD staying put, and your DS going to a state school.