First, the book is quite explicit about the fact that spouses weren't automatically "in" - the only way you could go to Galt's Gulch is if you were fully aligned with the Strikers' philosophy and took the appropriate oath yourself. As one woman told Dagney while she was in Galt's Gulch,
"They represent my particular career, Miss Taggart," said the young mother in answer to her comment, wrapping a loaf of fresh bread and smiling at her across the counter. "They're the profession I've chosen to practice, which, in spite of all the guff about motherhood, one can't practice successfully in the outer world. I believe that you've met my husband, he's the teacher of economics who works as linesman for Dick McNamara. You know, of course, that there can be no collective commitments in this valley and that families or relatives are not allowed to come here, unless each person takes the striker's oath by his own conviction."
With that said, there are a few possible explanations here, and the book doesn't conclusively establish which one is correct.
The first possibility is that she wasn't working at the time anyway. The book doesn't really specify whether she ever worked or, if she did, how productive she was. Once her husband retired, though, they started living on their savings (which implied that she wasn't working at the time that her husband retired). That being said, it may have been unnecessary for her to join the Strike. (This would be somewhat analogous to the case of Dan Conway, who never joined the Strike and doesn't seem to have been asked to join - although his case may have also been partially motivated by his moral philosophy, or by the fact that he had basically completely "given up" at this point - he was so badly broken by the Anti-Dog-Eat-Dog Rule fiasco that he completely lost his "will to fight," and Dagny believed that he would never be a man of action again).
The second possibility is that she wasn't fully aligned with their morality. Not being aligned with the Looters was decidedly not the same as being aligned with the Strikers.
The third possibility - which I think is the least likely, given William Hastings's marriage to her and his early knowledge of the Strike - is that it was an oversight on their parts. There were numerous people that were "overlooked" for a variety of reasons. (Notable examples include Cheryl Taggart, Eddie Willers, and possibly Dan Conway, although there could've been a number of different reasons that Dan Conway never joined the Strike - that's discussed here).
Another point (and this was probably only a minor point either way): the book is quite clear that she didn't really know John Galt; she only saw him very briefly on a train platform when her husband pointed him out to her.