"Cat-and-dog life" is a phrase that's often used to describe a volatile or difficult relationship, typically between people who are constantly bickering or fighting. There are a number of other synonyms that convey a similar meaning, including "rollercoaster relationship", "stormy relationship", "rocky relationship", and "tumultuous relationship". These phrases all suggest that the relationship in question is highly unpredictable and that the individuals involved experience intense emotional highs and lows. Whatever the term used, it's clear that a "cat-and-dog life" is not a pleasant situation to be in, and often requires significant work to overcome.