Everytime a person takes a job they have an opportunity to negotiate everything from salary to hours. Since nurse A has had these hours, I will assume it is part of "her" work agreement. If nurse B required these same hours it was up to her during her "negotiation" to make it a part of her package.
That being said, if nurse B requires those hours she needs to speak with management so she is not being penalized for lateness. I'm surprised she has waited this long. If management will not budge then she will need to do whatever is necessary to keep her job.
Does it sound fair? Maybe not, but deals like these are frequent in business. When I took my first job in ER, I had no experience, but refused to work nights. (Patient's would be in danger if I worked nights, as would commuters come am). Did HR like it? NO! I turned down 3 job offers prior to the manager giving me a day position. There were many applicants, but management thought I was worth it. My fellow nurses who oriented with me, all went to nights. Was it fair to them? Yes. That's what they signed up for.
I was a single parent during the time my children were young. It was tough. I truly understand the situation, but Nurse B will learn like I did. You need to fight for yourself and your family. Sitting back is only building a negative personnel file.