No couple is exactly what the textbooks would like to compare to. the end result of these events will entirely depend on this couple's dynamics between themselves, and with her family, as well as the priorities of the individuals involved.

On one hand, this could be her disengaging from a potential fight (not him, just the fight) because she has decided that "in-law time" is less important than "not arguing". The impact of this depends on whether this is just because she hates arguing, OR whether their particular situation makes "in-law time", even on holidays, relatively trivial in the greater scheme of things. If it's not IMPORTANT for either party for him to go, then avoiding the argument makes sense. Why fuss over something that doesn't matter that much to you?

However, if it is important for her that he goes and she has "given up" trying to get him to spend time with her family on a holiday, that bodes worse for their relationship. I can't say whether it will end in break up, but it will certainly lead to fighting and tension.

If this is a compromise over something relatively unimportant to her, then I think it would be a positive development indicating successful communication and compromise in a relationship.

If it's her giving up on something important to her, I think it is an indicator of a poor prognosis.