congrats on the mouselings.
When my mice have babies, I just clean the tank around the nest and leave the nest intact (I use upside down rubbermaid type bowls for nests.) The mothers are actually pretty clean in my experience; they exit the nest to defecate. So the inner part of the nest really doesn't have a huge fecal buildup. Once the babies have opened their eyes, everything gets cleaned as they're transferred into a bucket with mama.