In the United States, by federal law (HIPAA
), your privacy is very much protected. If you request it, your hospital cannot even tell someone whether or not you are a patient at the facility. You can also instruct hospital personnel that you do not want to have any visitors admitted. Don't wait to tell the nurses when you get there - it might be too late. If you pre-register (like I did), you can include this information in those papers. In fact, I think the paperwork I completed even asked what I wanted. If you have any questions, call the admissions department at the hospital you plan to go to, and see if they can help you.
And I third (fourth? fifth?) the suggestion to not even let your mother or any other family member know you're in labor. Call them when you are ready to see them. If they cannot respect you and your needs at this time, they don't deserve any special treatment or notice.