Psalms are
poetry. They're not supposed to be read as prophetic narrative, or even at all literally. They are texts of feelings, of introspection, of spiritual and emotional imagination, of imagery and metaphor and idiom and so forth.
Psalm 2 is a "Davidic" psalm, written in the first person, using language suggestive of the psalmist narrator being a king, and describing the fears of such a one surrounded by enemies. The second half of the psalm, in which the psalmist feels emboldened by his relationship with God he shows us how comforted he feels by that closeness. But the imagery he uses to describe it, in which it is as though God has claimed him like a parent claims a child, is just that: imagery. It's not that anyone-- the psalmist or otherwise-- is literally a son or daughter of God, but that when, in the course of confronting his enemies and fears, the psalmist feels as though he were so protected by God, it's as though God was his parent, and finds new courage and hope.
By the same token, in any kind of religiously-inspired poem, from any religious tradition, imagery is used that is not supposed to symbolize anything approaching literality. For example, if we read
John Donne's holy sonnet XIV, the poet compares himself to a beseiged town held by enemy forces, and urges God to overthrow the occupier of the town and "ravish" him (the poet). And we understand that this is imagery, representative of Donne's feelings, and his yearning for God: we do not suppose either that Donne was literally a town, nor that he desired God to rape or seduce him.
The only special connotation that this psalm might have, as far as I know, is that, like some others, it is held by the tradition to be a psalm that speaks well to those facing troubles in their lives, and is said to have virtue to comfort those in danger or in grievous need.