I'm surprised by the loathing for the Cotswolds on here - I absolutely love it and would move there in a heartbeat.
OP, you're getting a lot of stick for this, and I'm sure you chose the new area with your children front of mind rather than a breezy 'Well, we like it, so tough tits' attitude. Were the kids in favour of the move, and if so, what were the benefits that they could see? Is it worth revisiting those as a reminder for them?
We did something similar last year. We moved our DDs to a new school - private, and very different from the one they were at - in the hope that we could vastly improve their education, their opportunities and their world view. It backfired spectacularly as they were both deeply, deeply unhappy. It was hell, honestly, so I feel like I know to a degree how you must be feeling.
My advice would be, as hard as it is, stick with it for now but mentally, tell yourself that this won't be forever and you can move back if things don't improve. However, the biggie is not to go back at half term as this will be a reminder of everything they miss and everything they want, and it'll all be rose-tinted, and it will make returning back to the new area and new school ten times harder.
I know of so many families who moved and the children hated new areas and new schools, but stuck with it and now, looking back, they credit it as the making of them, and they will know that you did this for them, to give them a better life, a better opportunity. And, while it's shitty for them right now, this will teach them resilience and remind them how strong and brave they are. If however, it's genuinely detrimental to them, you'll know and it won't be a choice.
It sounds like DS is making friends and settling in, and sport is brilliant for that. For your DD, her age makes it harder, but there will be kids like her, she just has to find them, or let them find her. I know suggesting activities fell on deaf ears with my children, but the more she does things she likes, the more likely she is to find her tribe. And, once they have a friend, or two, or ten, life will feel a thousand times easier.
Try not to make a decision too quickly based on a rocky first few weeks. Remind yourselves why you moved, and remind the kids why too, and see what you can do as a family to help them fall in love with the benefits of living where you are.
Good luck!