usage of "in other words"

Solution 1:

It's hard to say for certain because the sentence itself is a bit confusing both in word choice/order and in punctuation. I imagine that the writer intended to indicate:

After stating that everyone's opinion can be different about this, for me honesty - in other words, always telling the truth - is the most important consideration in a relationship.

That's more parentheticals than I personally would care to use in a sentence like this. But the phrase "in other words" would not be inappropriate if my interpretation is accurate. It clarifies the intended, specific usage of the word "honesty" in the context of the sentence.

The writing would be improved by breaking some of these clauses into separate sentences, but that's off topic with respect to the phrase itself.