English Translation
No, no! That’s not right.
Is this phrase (どっこい) slang? Is it actually best translated as “No, no”?
@ericaw
どっこい is not slang but a slightly colloquial expression with several functions.
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As a conjunction – どっこい in this context is close to “but the reality is…”, “adversely” or “unexpectedly”. “どっこい。そうはいかないよ” means “(You probably expected X.) But X doesn’t work or X won’t happen.” いかない = 行く + ない, so そうはいかない literally means “it won’t go as you expected”.
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As an interjection – どっこい is used when you lift up something heavy (e.g. suitcase, standing up from a chair = lifting your own heavy body). There are some variations such as どっこいしょ; うんとこどっこいしょ.
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As a shout – You can still hear どっこい、どっこい in traditional festivals or folksongs. It’s probably close to “Hurrah!” or “Go for it!” to cheer up in English. There are some etymological theories behind this usage. One of the well-known ones is どこへ (to where) phonetically transformed into どっこい. The phrase is believed to be firstly used either in Sumo games（相撲）or Kabuki plays（歌舞伎）. Sumo wrestlers have a short performance before fighting in order to frighten the opponent. – It’s similar to “Haka” by New Zealand All Blacks’ performance in rugby games. Sumo wrestlers used to say to the opponents “Ha? Where are you going? Scared to fight against me?”
Back to your main question: What’s the best translation for “No, no! That’s not right.” I would propose:
いやいや！そうじゃないって。
違う、違う！そうじゃない。
とんでもない！それは誤解です。（ごかいです） Note: とんでもない = absolutely no; 誤解 = misunderstanding