Thanks everyone for the good advice but there are still a few snags.
The Lady in question has a Master's Degree. She does not have a Doctorate.
Everyone agrees that hyphenation is not an option. None of the names involved are common. Let's say that hyphenating her married names would make her name almost identical to that of the sculptor who created Mount Rushmore.
She has decided to go with the name of her second husband and will make sure that appropriate people are informed.
I think the advice would be the same whether she has a masters or doctorate. Obviously it wouldn't be Dr. Jones vs. Dr. Henderson, but rather Ms. Jones vs. Ms. Henderson.
The good thing nowadays with so many publications and records being online is that I think most journals have a way of connecting all the names that represent the same person, if they're kept informed. So with me, for example, Lynn Miller, Lynn A. Miller, and L.A. Miller should all point to me. Even better that her name choices are uncommon, she won't be going, "No, I'm the other
Lynn Miller!" all the time. For the journals she's published in, maybe she can check their websites and see if they have a FAQ or something addressing this question specifically. (Maybe that's what you meant by the "appropriate people" being informed.)