Translations depend on context. You can translate literally, use metaphors, ...etc, but it all depends on context and, especially in Japanese, the relation between the 2 interlocutors (level of speech used)
Usually you take the literal translation to get the general meaning:
あなたの私生活についてとやかく言うつもりはありません。
I have no plan to complain about your private life.
(とやかく meaning "this and that, all kind of things" here)
Then depending on the context, interlocutors, and situation you can find synonyms for "complain" like "quibble over", why not. It also depends on who you aim at with your translation.
The use of the ます/ません form in some cases can be sarcastic so there's nothing wrong using "give a damn" in English. (although there's あなた at the beginning, so this is less likely)
Tangorin gives these example sentences:
- 私個人の生活についてとやかくうるさくいうのはやめてください。
Get off my back about my personal life!
Let's not quibble over trivial matters.
She went on at me for coming home late.
NOTE:
I realize you say there was no context with the sentence.
I personally think this is not a harsh expression and shouldn't be translated as "give a damn" or "get off my back" unless the level of speech is lowered considerably. (あんた、おまえ、つもりない...etc.)
とやかく言う is a metaphor.
とやかく which original characters are 兎や角 shares the same etymology with とにかく and ともかく that you may have heard more often. (note that 兎耳 {うさぎみみ} is a gossiper (or someone with long ears) )
Etymology:
According to the following 2 links
http://gogen-allguide.com/to/tonikaku.html
http://gogen-allguide.com/to/tokaku.html
とにかくの「と」は「そのように」、「かく」は「このように」で、いずれも副詞。
Both と and かく are adverbs that can be written using 兎角 or 左右 independently from the meaning of the characters. (ateji)
wrong theory
I think the etymology of 兎や角 (and derivatives) comes from the Chinese expression:
龟毛兔角 = Turtles with hair and rabbits with horns = Things that don't exist, impossible
By stretching things a little, 兎や角言う could literally mean:
"talking about rabbits and horns" => gossip, fantasizing, making things up