I only don't move mice that are within 1-3 days old. After that, anythings fair game to be moved and cleaned. At work, mouse cages are changed every two weeks, and you scoop up the litter with some nest/dirty bedding and move them to the new cage. Unless mom isn't taking very good care of the little ones you shouldn't have any issues. 

I've lost a whole litter trying to clean them with in the first few days.. at a couple of weeks I think you should fair much better in the cleaning.  +1tmth

 Just change the bedding on your normal scedual  ..like brandon said  i just move them over no problems ..  i also  sprinkle powdered milk on thier food  helps moms recover  and stops them from eating babies

If you are losing babies it is usually due to lack of nutrients in the food or dehydration.  I started breeding mice 20 years ago and have seen a couple of litters.  I also worked for Rodent Pro before they were Rodent Pro.  Cleaning cages with fresh litters isn't going to disturb the females or babies. 

i've found that if you wait a few days, and then put some of the old nest material in the newly cleaned area, it helps a lot.

I clean once a week.If they have a new litter of babies I just clean around that area without disturbing the nest.If its really bad I will scoop out the babies and some of the litter and put them back exactly as they were when done with some of the stinky litter they were born in.

I have three of those little igloos they use for having babies in..I keep a colony of around 6 females and one or two males(Im actually not sure how many I have, Im guessing). In one giant 5ft bin.Ive not lost a single litter and none are eaten.I do keep them in very deep litter and hay because I have them outside, they make tunnels through it so thats why Im not sure exactly how many I have.I do check once a month and usually weed out any extra males.

The move was successful. No mass murder or massive carnage to report. Everyone took to it just fine. THanks for all the answers guys.