Jane and John are very concerned about their five-year-old

Since logically the five-year old twins can't be flying their parents, it is the parents who must be flying their children. So the pronoun ‘they’ must refer to Jane and John.

Secondly the object pronoun 'them' referring to the children is essential to make it clear that the parents are themselves not flying. These norms leave choices C and E.

E is wrong because of the use of the prepositional phrase 'on Sunday', which may tend to mean that the summer home is located on Sundays. Not a big issue but still C is more forthright.

They is referring to parents because 5 years old twins cannot fly themselves or their parents.

I fail to see how this is stylistically better than the original (as it still has the pronoun ambiguity). Moreover it changes the meaning.

The so-called meaning change introduced by adding the pronoun "them" actually improves the logic of the sentence and makes it less ambiguous.Without "them" we don't understand who will be flying to Vermont - Jane and John? Or the twins? The addition of them makes it clear that Jane and John will be putting the twins on a plane, and the twins will be flying to vermont.

Let's look again at the corrected sentence. Since the sentence contains a subject and an object: "They will be flying them" (meaning "they" will be putting "them" on an airplane) - logic requires that "they" refer to the adults - Jane and John - and that "them" refer to the five-year olds.

In the real world, this is the only imaginable understanding of the sentence. Of course, in an imaginary world, it could be different: the twins could pay for their parents plane tickets, or maybe even ride on their parents' backs through the skies to Vermont. However, the GMAT will only present you with sentences describing real-world scenarios.

Finally (and this can never be stressed enough) meaning change in itself is not a sufficient reason to eliminate an answer choice, as a small meaning change is often inevitable to correct the sentence. If the other answer choices have worse grammar or logic mistakes, they are preferable to answer choice that has only a meaning change.

Ans C- Why?

1. Pronoun must be unambiguous
2. Every pronoun has only one possible antecedent
3. Pronouns shows the tendency to refer to nouns in the same case. Ex above: a pronoun "them" which is in object position is presumed to refer to the object of the prallel clause "twins"

Hope this helps!

The object pronoun ‘them’ is essential to imply that the children are essentially traveling, mostly with the parents. A may tend to mean that the parents alone are traveling. Why will they travel alone? Are the going to attend a summer school on parenting?

To assume that the children might be already there is imaginativeness at its height.

SC’s one concern is effective expression through logical predication. I think as per this norm, A, though may be grammatically correct, is still inferior to C

I agree that end of the sentence is not the right place for the phrase ‘next Sunday’. It should go along with traveling. But all the choices falter on this; so let us ignore it.