MRSA infections can be very serious. However, a large percentage of the population (I think I've read as many as 1/3, but I'm not positive) carries MRSA in our noses but is not actually infected with MRSA. Some hospitals have taken to swabbing patients' noses to see who is a carrier for MRSA to try to prevent infection, which is what they did for your mom (your mom had this when she went into the hospital -- noses are swabbed on admission. It's also largely so that, if your mom develops an infection, the hospital can say "We didn't give her MRSA, she was a carrier when she came in!"). The reality is, though, if she were never swabbed, no one would know. She is not sick.
She should talk to the doctor about going to your home with the baby, but I wouldn't be too worried as long as she no INFECTION (if she had a MRSA infection, I would be very concerned). There's a good possibility you have it in your nose too and just don't know it. Most nurses probably carry MRSA in their noses, too, and yet have babies and all without any issues. But definitely talk to the doctors.
ETA: Oh, one other thing. The hospital will usually treat anyone who's positive for MRSA in the nose with nasal antibiotics. It's entirely possible that she went in with MRSA in the nose (so you've all been around it already) and doesn't have it after the treatment.