I think that your question about rephrasing Swift's sentence has its answer in literary, not grammatical considerations, so I answered it in my first comment. The issues you raise in your comments are grammatical, so I think they deserve an answer here, rather than in the comment thread.
The English infinitive is a difficult construct to master. It's a particular kind of verb, one that doesn't carry tense and thus doesn't tell us about time. (These kind of verbs are called non-finite, as opposed to finite verbs that are inflected for tense and do tell time). It's usually introduced by the word to, as with the Swift passage need to tell, but with certain verbs the to disappears:
[1a] I heard him tell a story.
which we analyze grammatically as
[1b] *I heard him [to] tell a story.
But with constructions like 1b, it is ungrammatical to actually use the to. (I've signaled this with an asterisk in front of sentence 1b.)
As a verb, an infinitive can take take a subject (the thing or person performing the action of the infinitive) or an object (the thing or person taking the action of the infinitive). In sentence 1a, him is the subject of the infinitive -- that's the person doing the telling -- and a story is the object of the infinitive -- that's the thing that's told. (Notice that the pronoun subject of the infinitive is in the objective case (him). This is different from the subjects of clauses with finite verbs. Those subjects are in the nominative case: He told a story.)
The infinitive itself cannot act as the verb in the predicate of a finite clause because it cannot carry tense to tell you about the time in the clause, but infinitives can perform the same functions as modifiers (adjectives and adverbs) and nouns.
An indirect object is different. An indirect object is the recipient of a verb of transfer, and it must appear with a direct object, the thing transferred. The most common verb taking an indirect object is to give:
[2a] I gave John a compliment.
John is the indirect object because he received the compliment; compliment is the direct object because that's what John received. We can also say in the same manner
[2b] I told him a story.
Again the indirect object him receives the story from me; the direct object story is the thing received. We can rephrase this to remove the indirect object without changing the meaning:
[2c] I told a story to him.
The story is still the direct object, but the recipient has moved to become the object of the preposition to. (That's the same spelling as the word that introduces an infinitive, but it has a different function.)
Finally, I'm ready to deal with the children and the stories. Recall from my previous answer that there are two way to express what's needed. The first is with the verb to need and a direct object:
[3a] I need water.
What I need is water, which is a direct object of need.
The second is with the verb to have with need as its direct object. In this case what's needed may be supplied with and a prepositional phrase with of, the object of which tells what's needed. I've placed the object of the preposition, water in parentheses
[3b] I have need of (water).
Or what's needed may be supplied by an infinitive. I've placed the infinitive in double parentheses:
[3c] I have need ((to drink water)).
Or the need may be expressed by both the prepositional phrase and the infinitive:
[3d] I have need of (water) ((to drink)).
Swift uses the have construction of the 3-sentences. Suppose he'd written
[4a] have need of (children to tell stories)
The infinitive clause has a subject (children) who do the telling, an object (stories), the things that are told, and the entire infinitive clause is the object of the preposition of. This is like sentence 3b. Remember that I said that infinitives can fulfill the functions of other parts of speech. So here, the infinitive serves as the object of a preposition just the way the noun water did in 3b. The meaning here is that the need is to listen to children because they're the ones doing the telling.
But Swift used the construction of 3d and wrote this instead:
[4b] have need (of children) ((to tell stories to))
At the last moment, with the final to, Swift has changed the meaning from the need to hear children tell stories to the meaning of telling stories to children. In other words his meaning is
[4c] have need to tell stories to children
The tricky thing is that in 4b children is the explicit object of the preposition of that is associated with need and the implicit object of the preposition to that is associated with tell. To make that implicit object explicit would require a clumsy rewording:
[4d] have need of children and to tell stories to them