Hi Sarah,
You're running into a somewhat-unavoidable quirk of automatically inserted variables in InDesign. What's in the flow of text is a code, and InDesign doesn't properly account for the expansion of the code into a piece of text. The code is a single character, and it behaves in some ways as a single character, no matter what the expanded text value of the variable is. As here, this can have unwanted formatting side-effects.
The solution, at least for now, is to use forced line breaks, “No Break” and soft hyphens in the surrounding text to bring things back to a reasonable appearnance. Sometimes you just have to type stuff by hand once the copy editing is final. To give you an example, a book I designed last year had an extensive glossary with Chinese characters appearing in certain entries. I used text variables to put the first and last definitions on each page as part of the page header, dictionary-style, which worked fine for the English-only entries. Because the text variable is in reality a single code, it can't have multiple fonts or styles, and unfortunately the font for the Chinese characters in the book was not the one I used for the main text, which was in English. Where an entry word showed up in the header, I had no choice but to delete the text variable and manually type that part of the header.
A similar thing to what you're seeing can happen where an automatic chapter title is part of the header. If the title happens to be longer than will fit in the frame, it won't overflow (because it's really only one character), but the expanded text won't fit, so InDesign squashes the text until it does. The solutions here are to expand the text frame or use a different chapter title.
More intelligent handling of inserted text variables is a great subject for a feature request! Add your voice to the clamor here at the Adobe website.