I see that Slanguage agrees with Patridge:

Twang (vb & n poss onomat). Fuck a woman; woman seen as sexual object. Hence twangman (n) Pimp. N.d. Anon. The Twangman: 'Come listen to my story,/Tis about a nice young man./When the militia wasn't wanting/He dealt in hawking twang.

It's unlike my mother - a dignified and elegant woman, but not one with great patience for unnecessary obfuscation - to make any mistake on something like this. It may be that 'twine' is what she herself was told as a child and young woman.