Yes you can. I suggest as you make up the new bed area you layer it so you can quickly change it.
I usually put several layers of newspaper and then something soft over it that won't absorb fluids but will let fluids through to the papers underneath. Typically I use polar fleece or fake sheepskin but people use a variety of things for that.
Then you can swap off the top covering and the top papers and replace as needed.
I'd set up a soft place for the pups, move them first, and then mom will move or can be moved over to where the pups are.
Then clean up the nest area and move pups and then mom back.
If the mother is too stressed to let you do that try giving her 250mg to 500mg of vitamin C and then see how she is in about 20 - 30 minutes as that can calm mother dogs down nicely.
If mom is too aggressive and you have a fenced yard you can make mom go out for a potty trip and then do the changing and let her back in.
Make sure the pups do not get chilled as at this age they cannot control their own body temperatures.
Hope this helps you!
I see you added more info as I was replying - do not wash the mom - you can trim off any dirty pantaloons fur if you want but washing mom will mean babies will be nursing on skin with detergents or flea poisons on it and that is not a good idea. Plus washing may introduce germs to the genital tract causing infection.