grabbing by the tail can cause injury to the tail, as well as 'skin' it away. Grabbing by the base of the tail (near the mouse's rump) is the best way to get them by the tail. Using a toilet paper tube, blocking each ends with the mouse or mice in side, is another good way. I typically play with my mice so they are not completely panicky when I come around to move them.
I find trying to grab tails of fleeing mice no more easy than just scooping them up in my hands then dropping them into another container for 'prepping' to be frozen or fed. Th is second container has no place to hide or bedding to get in the way of catching them, which makes it easier. I use the same for cleaning as well.
Once all the adults are gone, you can harvest the babies then remove the rest and put them in a smaller container with old clean rags or just sections of the nest, for the babies to cuddle in till you're ready to put them back into now clean cage. Once the adults are back into the clean cage, they tend to show less stress if they were there while you place or remove babies. Returning some of the original nesting bedding into the clean cage helps as well, so at least that area smells right to the adults. Leave them all alone after that to settle in and shouldn't have worried about mothers eating the rest of their young.
