I've never moved a nest, but I have taken some chicks away when I thought she could without so many. Didn't bother this particular hen. It makes sense that doing this at night would work better.
I agree with Ron, and once she's out and about with those chicks she isn't going to want to stay in one area. Plus if you are not sure the other eggs are fertile, you don't want to take the chance of taking away her babies, and then her possibly not wanting to go back to them.