Isaiah records the LORD's words:
... The heaven is my throne, and the earth is my footstool: where is the house that ye build unto me? and where is the place of my rest?
Isaiah 66:1 (KJV)
So, according to the LORD, heaven is where He dwells, and the earth is where He sets his feet.
David explains what God means by "my rest":
... Hear me, my brethren, and my people: As for me, I had in mine heart to build a house of rest for the ark of the covenant of the LORD, and for the footstool of our God, and had made ready for the building:
1 Chronicles 28:2 (KJV)
So, it's not God, Himself, who is resting in the Tabernacle or Temple, but the ark of His covenant.
Regarding the "footstool of our God", David is making reference to authority and rule. For example:
The LORD said unto my Lord, Sit thou at my right hand, until I make thine enemies thy footstool.
Psalms 110:1 (KJV)
In the NT James reinforces this notion of a footstool when he speaks of the unrighteous practice of respect based on wealth and influence that was happening in the church:
And ye have respect to him that weareth the gay clothing, and say unto him, Sit thou here in a good place; and say to the poor, Stand thou there, or sit here under my footstool:
James 2:3 (KJV)
So the Tabernacle and Temple were to be a resting place for the ark of the covenant (one mobile, for Israel only, and one fixed, for the nations of the OT world), and a place from which God would make His authority and rule known upon the earth (first to Israel and then to all the nations of the OT world).
The ark of the covenant of the LORD was a holy object and the central item within the Tabernacle and Temple, and the design of the holy place in which it stood has great significance.
Remember this: when the LORD put Adam out of Paradise he installed Cherubims to guard the way of return:
So he drove out the man; and he placed at the east of the garden of Eden Cherubims, and a flaming sword which turned every way, to keep the way of the tree of life.
Genesis 3:24 (KJV)
Well, Moses records God's words in regard to the Tabernacle of meeting:
18And thou shalt make two cherubims of gold, of beaten work shalt thou make them, in the two ends of the mercy seat. 19And make one cherub on the one end, and the other cherub on the other end: even of the mercy seat shall ye make the cherubims on the two ends thereof. 20And the cherubims shall stretch forth their wings on high, covering the mercy seat with their wings, and their faces shall look one to another; toward the mercy seat shall the faces of the cherubims be.
21And thou shalt put the mercy seat above upon the ark; and in the ark thou shalt put the testimony that I shall give thee. 22And there I will meet with thee, and I will commune with thee from above the mercy seat, from between the two cherubims which are upon the ark of the testimony, of all things which I will give thee in commandment unto the children of Israel.
Exodus 25:18-22 (KJV)
And 1 Kings records, concerning Solomon's Temple:
23And within the oracle he made two cherubims of olive tree, each ten cubits high. 24And five cubits was the one wing of the cherub, and five cubits the other wing of the cherub: from the uttermost part of the one wing unto the uttermost part of the other were ten cubits. 25And the other cherub was ten cubits: both the cherubims were of one measure and one size. The height of the one cherub was ten cubits, and so was it of the other cherub.
27And he set the cherubims within the inner house: and they stretched forth the wings of the cherubims, so that the wing of the one touched the one wall, and the wing of the other cherub touched the other wall; and their wings touched one another in the midst of the house.
1 Kings 6:23-27 (KJV)
When Moses writes, quoting the LORD, "... I will commune with thee from above the mercy seat, from between the two cherubims ...", the picture forms of God standing within Paradise speaking "between the cheribims" to man on the outside of Paradise. The ark of the covenant is thus the portal through which a holy God was to commune with His enemies in order to teach them His ways and draw them to Himself:
7Sanctify yourselves therefore, and be ye holy: for I am the LORD your God. 8And ye shall keep my statutes, and do them: I am the LORD which sanctify you.
Leviticus 20:7-8 (KJV)
So, all the many statutes surrounding the elaborate rites and practices in regard to the people and objects associated with the Tabernacle and Temple were specifically to facilitate this communion between Him who is holy and man, by virtue of his long history of separation, who is unholy.
By way of conclusion, then, the LORD never lived in a tent. His place of residence has always been heaven. The means by which He communed with man, however, needed to have a house, a resting place for the ark of His covenant.