The queen of Etruria was put into a convent with her daughter but her son was sent to live with his grandfather and she was not allowed to communicate with him for the next eleven months, after that only in limited manner. She, who was not officially a prisoner, was being kept under surveillance and her finances controlled; she seems to have communicated with the English in an attempt to get away with her children, which was understandable.
When Napoleon was sent to St Helena his wife had already separated from him and would not have joined him. It would have been highly selfish of him to expect the child to go with him and I don't think he seriously requested it. Anyone would agree the child was better off in Austria than on St Helena. Napoleon had been away from home for a large part of the child's life anyway.