Database
[{"name":"Guillaume","childrens":[{"name":"Robert","degree":"License"},{"name":"Michael","degree":"License"}],"students":[{"name":"Hélène","degree":"License"}]},{"name":"Mathilde","childrens":[{"name":"Lucie","degree":"License"}],"students":[{"name":"Michel","degree":"License"}]}]
Query
db.collection.update({"childrens.name":"Robert"},{$push:{"students":{"name":"Robert","degree":"Masters"}},$pull:{"childrens":{"name":"Robert"}}},{multi:true})