Please provide the source for that exact statement. It seems a bit limited and not directed towards the English word "emotion." i.e. do you have a source Hasidut that states "Emotion is an expression of a relationship."
The exact source? It's common sense.
Anyway, I provided you a couple of excellent sources for this already.
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The difference between G‑d’s attributes of intellect and emotion can be discovered through analysis of the functioning of these potentials in the human realm.
The working of the intellect does not require the presence of another person. Even when one is alone, without a second person with whom to share an idea, it is possible to think intellectually. The emotions, by contrast, require an object. The attribute of kindness, for example, requires a recipient of one’s generosity and kindness. If there is no recipient, the emotion itself disappears as if it never existed. This principle is reflected in a story the Torah relates concerning Avraham. He “sat at the tent door in the heat of the day”61 looking for wayfarers. He wanted to find someone to show kindness to, for without a recipient the giver loses this expressive potential.62
In this way we are helped to understand the statement that Torah preceded the world by 2000 years (and as explained above, this precedence is in spiritual level). The Torah possesses spiritual superiority even over the Divine source of the worlds. The Divine creative energy that creates the worlds only emanates from the middos of Hashem, in contrast to Torah, which emanates from Hashem’s wisdom.
Similarly, this principle can be understood in regard to the spiritual realms.
Hashem’s emotional attributes require, as it were, the existence of an entity that feels itself as separate from Him.
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As it turns out, the supernal emotive powers are the fundamental fabric of all things. And their most comprehensive expression within the entire cosmos is the fathomless depth of the human heart.
Of course, G‑d could have made a world that is no more than a dumb machine. Why did He choose to first manifest His light invested in these ten powers, and only then allow those ten to manifest themselves as a physical world?
G‑d could have said, "Here am I and, bang, here's a world. It works. That's good enough." But then it would be a dumb world, a world that explains itself, because, well, there isn't really much to explain.
That's not what He wanted. He wanted a world where its creatures could reach up to Him and He would reach down to them, until an affinity between Creation and Creator would develop and He could be found within His masterpiece.
So, He made a bridge.
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OK, so, we have the necessity for something seperate from Hashem, we have a bridge, we have the desire for us to reach up and for Hashem to reach back. And this is what defines the supernal emotional attributes. IOW, they are an expression of a relationship.