What are the chances of getting MRSA in a hopsital while you're there to have a baby?

Less than outside. At least in the hospital they pay attention to infection control. The MRSA staph are around us in our daily lives. They represent 70% of the pustules acquires by patients presenting to office clinics. Whether it is the supermarket cart or the doorknob at home, it is around us. Good hand washing & personal hygiene are important for everyone. I'd worry more about getting enough sleep for the job ahead.
Usually Benign Bact. Varies widely, donotpanic. Staphylococcus aureus frequently present skin & respiratory tract, especially nose. Mrsa merely means resistant multiple abs. Control of bacteria, as with all, a function of immune system. Sa most commonly a commensal bacteria, but reality not good for marketing fear. Dietary choices, activities, emotions, any internal control affecting staph & immune function can change.
Varies.... ..From region to region, state to state. Your hospital should have that information, as should your state regulatory agency. As a general rule, though, that risk is pretty small; the obstetricians and nurses all wear sterile gowns and maintain scrupulous sterile technique for the specific purpose of preventing any infections, including mrsa.