Sounds like you're stressing her out by checking on her too much. Her picking up the babies and moving them..as well as her avoiding the nest are signs of stress in mice. Not going back to the nest is an instinctive behavior so as not to lead the predator (Namely us) to her pups. Moving them around means she doesn't feel comfortable. Too much stress and she may, most likely, cannabilize her litter....
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Lucien
1.1 Columbian Redtail Boa (BCI)(Sutekh and Isis)
2.2 Leopard geckos (2 Blizzards (Caine and Goliath), 1 het Blizzard (Lilith) and 1 Tangerine Albino (Tequila Sunrise ...Tiki for short))
0.1 Savannah Monitor (Kiros)
13 rats
5 Gerbils
2 Dogs (Loki and Storm)
2 cats (Sahara and Hercules)