I have doubt where to put "is" in the following sentence:
"Their unique structure is among other due to that they are designed for rotation of the skull."
or
"Their unique structure among other is due to that they are designed for rotation of the skull."
A couple of corrections, first:
Among other is not idiomatic English.
When other is deployed as a nominal it requires a determiner if singular (another, the other, some other) and must be declined as others if it represents a plural referent.
And in this case, where there is no obvious referent to which other can refer, you have to treat other as a determiner and supply a head. Usually we say among other things.
Due to cannot take a clause headed by complementizer that as its object; you must employ a noun phrase or a gerund or fused relative clause:
∗ . . . due to that they are designed for . . .
ok . . . due to the fact that they are designed for . . .
ok . . . due to their being designed for . . .
ok . . . due to what they are designed for, . . .
Let me now rephrase your question. At bottom the issue here is not where is goes, but where among other things goes. Among other things is a supplement to your ‘base’ sentence; let's use the gerund clause version:
Their unique structure is due to their being designed for rotation of the skull.
What is it you want among other things to modify? Do you mean that the structure is just one of several things which is attributable to the design? Then you want this:
Their unique structure, among other things, is due to their being designed for . . .
But if you mean that the design is just one of several factors contributing to the structure, you want one of these:
Their unique structure is, among other things, due to their being designed for . . .
Their unique structure is due, among other things, to their being designed for . . . †
Other possibilities for locating among other things are these:
Their unique structure is due to their being designed, among other things, for rotation of the skull.†
Their unique structure is due to their being designed for rotation of the skull, among other things.
These two indicate that the vertebrae are designed for additional purposes.
Among other things, their unique structure is due to their being designed for rotation of the skull.
This one might mean almost anything, including the presence of things you want to say about these vertebrae which have nothing to do with either their structure or their purpose.
† Note that in strict logic the among other things ought to follow the preposition in these two: “due to, among other things, . . .” and “for, among other things, rotation . . .”. But in practice we really dislike separating the preposition from its object like that, and we write it as I have written it; practice trumps logic.
