The title you give to your question seems to indicate that you are confusing the two roles of to:
the infinitive marker
a preposition (often used in idioms where it is not easily definable semantically)
Making your sentence a little less complicated, to illustrate:
We want / need to allow client access to certain documents.
Want and need, as is the case with some other similar verbs, may be used in catenative constructions with other verbs:
I want to go.
He needs to ask.
He seems to think so.
These verbs require the 'to-infinitive' rather than the 'bare infinitive', the base form of the verb (actually, need can be used with the base form in some situations).
Help and dare may be used in some situations with either the to-infinitive or the bare infinitive:
he didn't dare to go / he didn't dare go
she helped to wash up / she helped wash up
dare you go? /*dare you to go?
In your sentence, to authorize is a to-infinitive, as is my to allow.
However, my sentence also contains access to certain documents, where to is a preposition. It forms a collocation with access (we always would say access to rather than access for, or access over, the documents).
Omitting the preposition to from my sentence leaves:
** We want / need to allow client access certain documents.* (access of course is still a noun here) It is obvious in this example that the preposition to is required; this is also true for your example, though inserting it at the end of the sentence results in a correct but clumsy-sounding sentence:
The interface offers the option to pick which ones to authorize client access to.