I think the meaning here is that before pulling the garment on she ‘snapped it’ to straighten it out - like you might do with a pair of trousers that are all creased up before pulling them on, or with a sheet or blanket to straighten it out over the bed. It’s the action of snapping something sharply with your wrists to make it straighten out so it can be more easily used, another example would be ‘snapping out’ the ground sheet of a tent after taking it out of a tight roll, to get the creases out of it.

That means "pulled it out abruptly" or "yanked it out." This is not a stable idiomatic expression but more of a poetic language.