In general, the Torah places a lot of supremacy to the spousal relationship in marriage, compared to other relationships, and one must generally put one's spouse first over almost any other commitment, including (generally) serving one's parents.
At times, we might have to attend to our spouse at the cost of another obligation, in a circumstance that couldn't have been foreseen or was otherwise not possible to control. How do we explain to the other party.
To keep it narrow let's just say we are dealing with a very standard case:
The husband is due to meet a friend for lunch - nothing urgent or important, but the other party has arranged their schedule to meet. At the last minute, his wife tells him she needs to talk because she is upset about something, nothing life or death, but important to her. The husband must inform the person he is meeting for lunch that he can't make it. How should he explain it?
Factors such as, Tznius1, Lashon Hara2 or Lo Titen Michshol3, Kedusha4 and more come to mind, which make it difficult to reveal much about why one must cancel the obligation in order to attend to the spouse.
What are tactful ways brought down either in written sources or stories of tzaddikim that illustrate how one should walk this fine line of dealing with such situations?
1 - it is immodest in halacha to discuss matters that are private between the husband and wife, and this covers a lot of ground, and might include even a simple statement like "my wife needs me"?
2 - by cancelling the appointment, one is doing something that's less than ideal, and looks bad if the full reason is not given, so saying just "it's because my husband needs me" could sound like LH towards the husband?
3 - saying "I have to cancel today, my wife needs me", without giving further information might tempt the person hearing this information to wonder why, and this may lead to negative thoughts. Anything from "she is controlling" to "I wonder if she has some medical condition" ch'v.
4 - similar to the immodesty point, the sanctity of marriage is an overarching principle that requires preserving in many subtle ways.