As someone who has moved multiple times, pre children and then with children, it is much more difficult with children.
That said, any move no matter how far, takes far longer than one year to settle. You are in a very negative mind space, so in that, you are not open to accepting the change.
Of course it is a huge change. I am not sure why people think things are the same no matter where you live. It is most definitely not, and you have to adjust to the new lifestyle. One year is not enough time OP. You haven't given it a long enough chance yet.
Also, if course you haven't a strong bond with friends. You haven't been there long enough to.
Your child who wants to move home. At 8 years old, why have you implied this is an option? As by doing that, you are allowing them to believe they also don't have to accept this new change and can just go back to how school and life was a year ago. Even if you do go back, it will still be different to them from how it was last year.
I can see you DH pov. It is such a big move and you haven't integrated as well as he has yet.
Him being at work had a huge amount to do with it. He is with the local people all day, learning the ways, meeting new people and getting on with it.
While you stay at home and do the odd camping trip and some socializing, I assume child orientated.
Can you see the difference? Why are you so anti childcare? I think that is the absolute best thing you need. Go and seek out a part time job and integrate yourself into the real lifestyle more.
One more thing. It's winter now. All of us in the SH battle a bit more in winter. We don't have the luxury of central heating and do tend to spend with winter months cooped up a bit more. Which is a vast change from the rest of the year when it's easier to do outdoor things. Never ever make a hard decision in winter is my motto.
You are setting your mind on the fact you miss your family. And that is your full focus. Shift it to being a bit more positive and acceptance of change. Otherwise you are never going to be happy. You will stay there with DH and be miserable, or you will return to UK single and still have to deal with some change.