This is a question that can only be answered by your mother’s surgeon. There are some types of neck surgery that don’t require bracing and others that leave it up to the doctor. However, there are also neck surgeries that absolutely require a neck brace or collar for a specific amount of time afterwards.
If your mother won’t go see her doctor, you may try to call the office to see what you can find out on your own, but this is really something that needs to be seen about by a healthcare professional, in person.