I'm not sure how long you've been living in London but from my experience, there are so many English living in Scotland and Northern Ireland now, to the point that when I'm there I hear more English than I do Scots or Norn Irish.
I think most English have integrated well, things have moved on and less hostility these days (generally speaking).
OP I have relatives on an island off the west coast of Scotland, so don't have experience of living there myself, but we do go stay with them. We really love it there, but the midges are a fucking killer. Our relatives, one is Scottish but has an English accent, the other is English, both have spent more of their lives living in Scotland. They utterly adore Scotland and love their island life, they are well immersed in their local community.
That said, the winters are harsh, the ferries situation, the cost of the ferries, the length of time to reach the mainland - huge ferry queues in tourist season. Campervans and tourists everywhere. They are getting old now, and have long trips to the hospital. They may potentially move off the island when they get elderly, but I know it would break their hearts to leave their wonderful home there.
Lots for you to think about, I think it would be worth you renting a place there for a year to see if you can handle the winters and the isolation.
As it happens, we home educate too. There will most likely be other children on whatever isle you choose, and there will be ways for your child to make friends. People still seem to think that home educated children don't socialise with schooled children which is silly as all of my children's friends are schooled!