The “Shechinah” is usually understood as “God’s Presence.”
But — Is God’s Presence something separate from God?
If God’s Presence fills the whole world, why the need for a Mishkan — later the Temples?
The Shechinah isn’t something separate from God. It’s the experience we have of God’s Presence. Although God fills all of Creation equally and evenly, it’s not something we experience equally at all places and times.
God doesn’t change, but our experience of God’s Presence can change, depending on our own internal and external conditions.
The gift of the Mishkan and Temples was that God gave a place where the Presence could be felt despite our status.
The Presence of God is not a theoretical thought or idea. It is a personal experience: The experience of our own highest delight; our “Eden.”
“In Your Presence is the fullest of joys.” 
As Rebbe Nachman tells us:
“There was once a king who had six sons and one daughter. This daughter was especially dear to him. He loved her greatly and took the utmost delight in her. One day when he was with her, he became angry with her. Suddenly the words slipped out of his mouth: ‘Let the Evil One take you away!’
That night she went to her room, but in the morning no-one knew where she was. Her father was very distressed and he went searching for her everywhere.” 
If we apply a strictly kabbalistic interpretation of this story, especially based on the Zohar, the “king” is the uppermost 3 sfirot, whose 7 children are the 7 lower sfirot, culminating in “malchut,” which is feminine in character.
“Malchut” is elsewhere synonymous with the Shechina.
In the Zohar, “Malchut” is the “Queen” who receives the “Shefa” — the vitalizing essence or energy — from the “King” for the purposes of creation.
Yet in Rebbe Nachman’s story, the “Shechinah” or “princess” is the daughter, not the wife, of the king.
Also, nowhere in Kabbalah, as far as I know, is the upper level of the sfirot held responsible for “banishing” the lower level, especially Malchut.
So, although Rebbe Nachman might have been borrowing imagery from the Zohar, he was applying it in his typically idiosyncratic way.
In this case, I suggest that the “king” is, in fact, ourselves, especially our Divine Soul — our own highest Divine essence — and the 7 “children” are the effects our actions create through interaction with the Divine, the sfirot being the medium of interaction. The effects of our actions are our “children,” as it were; we, ourselves, create them.
The king takes “utmost delight” in his daughter, the princess, just as the Shechinah, our experience of God’s Presence, is our highest delight.
“One day when he was with her, he became angry…” — We’re always “with” the Shechinah; always in God’s Presence.
Why does the king become angry?
Rebbe Nachman doesn’t say. But his point is not ‘why’ the king becomes angry. It’s that the king becomes angry at all and, in that very moment, speaks irrational words.
We, similarly, become frustrated when we find our own will in conflict with God’s; when we do not accept all that happens to us as God’s Will for the Good.
“One who becomes angry is like one who worships idols.” 
Accepting all that happens as being God’s Will for the Good can help bring us to the experience of God.
Becoming “angry at God,” we “banish” God’s Presence from our awareness. What do we lose? We lose the experience of God’s Presence. God remains no less present in our lives; it’s our own awareness that we have limited. Then, we “don’t know” where God is, just as no one knew where the princess was.
How do we become re-united — “reconciled,” as it were — with the Shechinah?
In Rebbe Nachman’s story, this is effected by the king’s “Prime Minister,” who might be intended to represent the “Tzadik” — the primary spiritual teacher. He might, in fact, represent Rebbe Nachman himself. What does the PM do? He travels and wanders almost endlessly, having intermittent contact with the princess, until bringing about the desired reconciliation. He is the “healer,” the “seeker,” the one who leaves his home and the place of his status, for the sake of the king’s happiness.
We find something of this in every true teacher who enters our lives. But the one who gives us the greatest spiritual guidance does the most to re-unite us with our “beloved child,” our “princess;” our own experience of God’s Presence.
 Tehillim/Ps. 16:11
Mine isn’t the only possible interpretation. Rebbe Nachman might also have meant the “Lost Princess” to represent “Israel,” whose soul, in Kabbalah, is the Shechinah; the “K’nesset Yisrael.” In this case, the “king” would represent God who becomes angry and banishes Israel from the kingdom. The Prime Minister then becomes the messenger of God, the tzadik whose role is to locate Israel wherever they are — especially spiritually — and return them to their home with God.
But in the story, the princess is guiltless and the king’s words are born of irrational anger. This wouldn’t mirror Jewish history, in which God’s banishment of the Jews (twice) was not due to “irrational anger,” but to provocation from the Jewish people ourselves.
 Shabbat 105b