This is NOT a case of tmesis. The modifier, nother, has been in use since the fourteenth century. It appears, for example, in the fourteenth century Northumbrian poem Cursor Mundi:

In-sted o þi noþer sede, Ne sal þe groue bot thorne and wede.

It also appears in early versions of the bible:

This kynd can by no nother meanes come forth, but by prayer.

Here's an example from David Crockett's An Account of Col. Crockett's Tour to the North and down East, in the year of our Lord one thousand eight hundred and thirty-four … Written by himself, 1835, Carey & Hart:

I'll now answer one nother question about what's the best way of keepin the democratic party in my quarter from splittin.

This word now appears chiefly preceded by the word whole in modern American and British English. However, it survives in freer usage in Caribbean English. Here's an excerpt from Richard Allsopp's Dictionary of Caribbean English Usage, 1996, OUP.

Peter and your nother brother were here today.

Notice that in all of these examples the word nother is not preceded by the indefinite article "a". The word nother is not a part of the word another with the infixing of an adjective. It's an extant word in its own right. It is easy to see however how that erroneous view could come about!

Given that this word has been used as a modifer in this way for eight centuries now, it obviously a bit backwards to consider it an improper usage. Such phrases as * a whole nother kettle of fish* are, of course, perfectly grammatical. Of course whatever native speakers generally do is grammatical. That's what grammatical means!

Note: All this information, including quotes, is taken from the Oxford English Dictionary.

References: "nother, adj.2 and pron.2." OED Online. Oxford University Press, June 2015. Web. 7 July 2015.

This is NOT a case of tmesis. The modifier, nother, has been in use since the fourteenth century. It appears, for example, in the fourteenth century Northumbrian poem Cursor Mundi:

In-sted o þi noþer sede, Ne sal þe groue bot thorne and wede.

It also appears in early versions of the bible:

This kynd can by no nother meanes come forth, but by prayer.

Here's an example from David Crockett's An Account of Col. Crockett's Tour to the North and down East, in the year of our Lord one thousand eight hundred and thirty-four … Written by himself, 1835, Carey & Hart:

I'll now answer one nother question about what's the best way of keepin the democratic party in my quarter from splittin.

This word now appears chiefly preceded by the word whole in modern American and British English. However, it survives in freer usage in Caribbean English. Here's an excerpt from Richard Allsopp's Dictionary of Caribbean English Usage, 1996, OUP.

Peter and your nother brother were here today.

Notice that in all of these examples the word nother is not preceded by the indefinite article "a". The word nother is not a part of the word another with the infixing of an adjective. It's an extant word in its own right. It is easy to see however how that erroneous view could come about!

Given that this word has been used as a modifer in this way for eight centuries now, it's obviously a bit backwards to consider it an improper usage. Such phrases as a whole nother kettle of fish are, of course, perfectly grammatical. Of course whatever native speakers generally do is grammatical. That's what grammatical means!

Note: All this information, including quotes, is taken from the Oxford English Dictionary.

References: "nother, adj.2 and pron.2." OED Online. Oxford University Press, June 2015. Web. 7 July 2015.