Rabbit breeding? Is it OK to move a nesting female or do you always remove the male?

I would move her, as long as you move her nest and any of her things that have her smell on she won't worry too much. She sounds like she would be much better off in the new hutch, and wire can be lethal for young kits, if they get onto it they don't get back into the nest and quickly die. Better for her and the babies if she goes into the new cage. Good luck, hope she has a trouble free birth!