I agree with others that the baby might not be getting enough food. It can be difficult to tell, especially with BF babies, how much they're getting.
It's important for the mom to know that all babies spit up--it's perfectly natural and doesn't harm them. My oldest spit up some, not a lot--she was formula fed. I nursed my second, and he spit up ALL THE TIME! Constatnly! I had burp cloths all over the house. I would have to do laundry, just because I ran out of burp cloths. It was nuts! But, it was just him. My younger two were more like my oldest--occasional spitting up, nothing serious. FTR, #2 is now 19, 6 feet tall, and weighs 200 pounds. It kills me, because he had such a sensitive tummy as a baby, and now he eats everything that isn't nailed down.
Hopefully, this baby has a 2-month check-up coming up, and the pediatrician can evaluate if she's growing adequately. Feeding can be a tricky thing--I failed at nursing my oldest, succeeded with #2 and #3, and then had to supplement with formula for #4. Apparently, I don't produce a lot of milk, and my middle two were aggressive enough to get what they needed. It is not maternal failure to struggle with proper feeding.
Another thought, in this particular case. Since the mom works for herself, might it be worthwhile to bring the baby and sitter to work with her? That way, she could nurse whenever. I have no idea if this is a possibility.