[{"id":"p00","children":[{"id":"c00","value":true},{"id":"c01","value":true},{"id":"c02","value":true}]}]

db.collection.update({"id":{"$eq":"p00"}},[{"$set":{"children":{"$map":{"input":"$children","as":"c","in":{"$cond":[{"$in":["$$c.id",["c00","c01"]]},{"$mergeObjects":["$$c",{"value":false}]},"$$c"]}}}}}])