What could the King of Pentacles mean when representing a relationship/relationship outcome between two people? To me, this card is earthy, grounded, prosperous, and represents stability, material and otherwise. What's confusing is that the relationship in question is currently not that stable,
It's not about whether the PERSON is stable, it's about the relationship. Unstable people who fit well together can be completely chaotic, yet have very stable relationships.
and the two people are reconciling after not speaking for a while.
Again, that doesn't seem to matter to me all that much. Time apart can give you a sense of proportion, which can allow you to either leave for good, or settle own with someone in the longer term, having had space alone to think.
On the other, it's not a very emotional card. Thoughts?
Of course it's an emotional card! The archetypal King Pentacles loves deeply enough to provide a safety-net for his lovers and family, he is their rock, he stands as a shield between them and trouble, he is grounded and solid in their lives, he is never disloyal, he opens his "castle" to them forever.
Of course, when they get tired of him and want to leave, he's not good at letting go, because his love doesn't end when theirs does.