Uniquity

Was talking to a friend about divorce, and how it "covers a man with violence like a garment" (Malachi)

It really does. Considering that according to the natural order of things the nuclear family is the basic social reality of every human being, not to have that is a serious disorientation.
You have a relationship that brought about your existence, which no longer exists. It's a lot like being orphaned, or very-late-term aborted. Every kid's existence is due to two other people coming together in at least one act of intimacy, and human societies have on the whole always recognized the need to formalize and turn into a sacred thing that bond. Children formed within it are "legitimate"; ones outside "illegitimate". Not "less human", but there really is something lost - a missing component of reality, a personal "Genesis" story that's lost. A child that has no Eden to point back to and say "that's where I came from, that's the place I was born" has a certain amount of psychological solipsism to deal with. They have no anchor, they are left floating in a sea of strangers, with whom they can form horizontal social bonds, but without a stable social foundation to rest on.
Even having one parent, or two parents separated, isn't the same. That reality which brought you into the world has been annihilated - it's like those Sci-Fi plots where Earth is destroyed and the human race is left orphaned and wandering in the galaxy, forced to make a new earth for themselves, a new home. But it will never be earth.

But with God, there is solace. It's said truly that 'Father of the fatherless and protector of widows is God in his holy habitation.' (ps. 68:5)

This really works. Even a human adoption, or the striking out into the void to make a new family for oneself, doesn't provide a child of divorce with a present reality continuous with their real origins. And that's a real loss. God, on the other hand, does. The child of divorce may be physically the product of gametes from a pairing that no longer exists. However on another level, "...you formed my inward parts; you knitted me together in my mother’s womb."(ps 139) is a real, true, ontological statement. By faith we know that we exist for God's pleasure and by His will, and in Him we can find an even more fundamental and solid grounding than that of a human marriage. The loss is real, yes, but so is the gift that fills the void.