Your answer to your mother in law would depend on your family dynamics and the relationship you have with her. If you love your mother in law, and would like to fulfill her wish of seeing her grandchild being born but just can't imagine going through labor and delivery with her in attendance, it is maybe even harder than if you really disliked her. If you are worried about your privacy and don't want your mother in law to see you in such a vulnerable position, you could consider allowing her to come to part of your labor, and then to have her come back once the baby is born.
Many women are worried that they'll be distracted by others' presence, and if this is you, honesty is the best policy. Stress certainly has the power to stall labor, so you could point this out. Saying that you love your mother in law, but see labor and birth as really private moments for you and hubby (plus medical staff) is also totally acceptable of course. Now, what if you really dislike your mother in law, or have a rough relationship with her?
Perhaps it's best that your husband talks to his mother about her request to be at your baby's birth. He can say that she'll get to spend plenty of time with her grandchild later, but that birth is really a matter for the immediate family. Don't feel pressured into doing something you are uncomfortable with not this time. Your baby's birth is so important. Your mother in law shouldn't ruin it for you.