I am wondering if it is correct to interrupt a prepositional phrase, or if it must be placed afterwards as a relative, or both, or something else.

Example:

... between what he called the right and the left ...

To see the English in a different way:

... between, what he called, the right and the left ...

... idir na rudaí a thug sé an eite dheis agus an eite chlé orthu ...

... idir an eite dheis agus an eite chlé a thug sé orthu ...

1 ...idir na rudaí ar thug sé an eite dheis agus an eite chlé orthu...
2 ... idir an eite dheis agus an eite chlé mar a thug sé orthu...

Though I don't think "na rudaí" will be the best way to translate "what". What's the context? What does "what" refer to?

It's simply a figure of speech. Here is a similar use:

It is widely believed that Hardy considered applied mathematics to be ugly and dull. Although it is true that Hardy preferred pure mathematics, which he often compared to painting and poetry, Hardy saw the distinction between pure and applied mathematics to be simply: that applied mathematics sought to express physical truth in a mathematical framework, whereas pure mathematics expressed truths that were independent of the physical world. Hardy made a separate distinction in mathematics between what he called "real" mathematics, "which has permanent aesthetic value", and "the dull and elementary parts of mathematics" that have practical use.

(Message edited by seánw on March 07, 2011)