The phrase "τί ἐμοὶ καὶ σοί" occurs a number of times in the Septuagint: Judges 11:12, 3Kings 17:18, 4Kings 3:13, 2Chronicles 35:21.
The NRSV translates the Hebrew of these verses as "What is there between you and me?", "What have you against me?", "What have I to do with you?", "What have I to do with you?". Someone knowledgable in Hebrew will have to comment on that, since I can't say anything else about it.
The related phrase "τί ἐμοὶ καὶ ὑμῖν" occurs at 2Kings 16:10, 2Kings 19:23, where the NRSV translates the Hebrew as "What have I to do with you?" in both places.
In the New Testament, the phrase "τί ἐμοὶ καὶ σοί" is used at Mark 5:7, Luke 8:28, and John 2:4. The variant from "τί ἡμῖν καὶ σοί" is used at Mark 1:24, Matthew 8:29, and Luke 4:34.
Achilles Tatius 6.12.3 has "τί ἐμοὶ καὶ Θερσάνδρῳ κοινόν;" The Acts of Andrew may have contained a similar phrase (v. 18), and is traditionally by Tatius, who the Suda claims became a Christian and a Bishop. (!!)
Of the New Testament usages, the odd one out is John 2:4. The others are all in the mouths of demons, but here it is Jesus himself, saying something rather odd to his mother:
The LSJ gives examples of γύναι as a respectful address "as a term of respect or affection, mistress, lady, E.Med.290, Theoc.15.12, etc." But τί ἐμοὶ καὶ σοί, if it means the same thing as it does everywhere else is very strange. It's a strange thing to say to Mary and her reaction makes no sense.καὶ ὑστερήσαντος οἴνου λέγει ἡ μήτηρ τοῦ Ἰησοῦ πρὸς αὐτόν οἶνον οὐκ ἔχουσιν καὶ λέγει αὐτῇ ὁ Ἰησοῦς τί ἐμοὶ καὶ σοί γύναι οὔπω ἥκει ἡ ὥρα μου λέγει ἡ μήτηρ αὐτοῦ τοῖς διακόνοις ὅ τι ἂν λέγῃ ὑμῖν ποιήσατε
I think the explanation is that we've locked ourselves a little to slavishly to a single use of this phrase. The New Testament usage is basically the same context every time, and the Septuagint isn't much better. The above isn't really a varied set of examples at all. It's almost a single data point.
If we're just willing to read this phrase as Greek, it becomes easy to see what is going on. John is using substantially the same relation between τί and the dative as the idiom elsewhere, but with the difference that his "καί" indicates hendiadys. It's a perfectly normal modification of a phrase. Jesus is saying "What is it to you and me?", ie. "that's not a problem for you and me." Remembering that his "hour" is one suffering and deprivation -- not glory and miracles -- makes the rest straightforward. Jesus is actually affirming to her that he is going to act to take care of things, just as Mary's reply following seems to imply.