What word does your mother always say?
c.1300, from frequentative form of stem of Old English verb swifan "to move in a course, sweep" (a class I strong verb), from Proto-Germanic *swipanan (cf. Old Frisian swiva "to be uncertain," Old Norse svifa "to rove, ramble, drift"), from PIE root *swei- "swing, bend, move in a sweeping manner." Middle English swive was the principal slang for "to have sexual intercourse with," a sense that developed c.1300. This probably explains why, though the root is verbal, the verb swivel is not attested in Modern English until 1794. Cf. Middle English phrase smal-swivinge men "men who copulate infrequently."
1794, from swivel (n.). Related: Swiveled; swiveling; swivelled; swivelling.