Your mother in law may have been discouraged from breastfeeding her children, told she wouldn't have enough milk, and not understand the mechanics of breastfeeding. Perhaps it will help if you copy some of the common sense information from kellymom.com or the La Leche League website so that she can see it.
She may also be thinking that if you are breastfeeding, she will never be able to care for the baby. Try to include her-as much as you can-in other aspects of baby care if it is appropriate. She may not be able to feed the baby for the first several months, but there are certainly other things she can do. She may also be concerned that her child-the baby's father-will feel left out, or that breastfeeding will 'tire you out', especially as she doesn't understand it.
And MIL obviously does not understand that breastfeeding is normal, and that babies and mothers who breastfeed have normal-and not ill-health. She may not know that babies who are not breastfed are sick more often in the first year, more likely to die in the first year, and more likely to suffer from diabetes, high blood pressure, and certain cancers, as are their mothers. Again, offering her some printed information (you might say it's 'from the doctor') may help.
Good luck with your new baby and your MIL.
hospital IBCLC and mothers' group leader 20+ years
mom to 3