it's a really good idea to not remove or disturb the nest until the pups are weaned. whenever i had a mom who was getting ready to burst... i would clean the cage, and then, just leave it alone. IF i needed to clean the cage... i would clean everything but the nest... i wouldn't move it, just clean around it.
the male should, of course, be removed before she births as she can become pregnant immediately after giving birth and that's not good for her health.
here's a link for you with some great info.
http://www.horns.freeserve.co.uk/mouse.htm