Hi tuitui and Welcome to BYC!
I can tell you about my experience with broody hens hatching eggs. But I think that getting the right solution for you always depends on your own circumstances.
I had two broody hens who hatched eggs at the same time. In fact, I split the eggs between them. I did not separate them, and they did fine. That said, they had loads of room and weren't crowded in the least. Also, they were "buddies". One hen left her chicks before the other, and the chicks just went over to the other broody and became hers. No problems at all.
As for moving them, I've done it both ways. I moved hens and eggs, and it was fine. But I was quite worried that the hen would be upset and leave the eggs. Just like you are. And I've waited until the eggs hatched and moved hen and chicks. That worked fine, too.
I think I preferred the moving of the hen and chicks, just because it is a possibility that the hens might stop sitting. Very worrisome. They hate change. Didn't happen to me, though.
I think that one depends on whether you need to move them now or not. Are they hogging up nestboxes that your other chickens want to use? That's a nuisance! Some other reason?
Just some thoughts I had on the subject. I'm sure you'll get loads of advice on this. And good luck with your hatch, whatever you decide to do.