For full context: http://www3.nhk.or.jp/news/easy/k10011218521000/k10011218521000.html
The sentence in question:
「中国やロシアから旅行に来る人がビザを取りやすくなったり、韓国や香港などとの間を飛ぶ飛行機が増えたりしたためです。」
"This is because it became easier for travelers from china and russia to get visa and because the number of aeroplanes flying the space between korea, hongkong and so on has increased."
Why is it 韓国や香港などとの間? Why is this と there? I would've expected a mere の.
Let us first get the basics down by looking at a simpler phrase. How do you usually say something like "the border between France and Germany"? Native speakers say:
「フランスとドイツの国境{こっきょう}」 informally
and
「フランスとドイツとの国境」 formally. ← Needs two と's!
Thus, the formula here is:
"A + と + B + との + Noun"
We do use that second 「と」 when speaking/writing more formally, and I know from experience that quite a few Japanese-learners are not aware of this. Since you seem to be reading the news, you would naturally encounter more formal phrases and expressions.
Now, the actual phrase in question.
「韓国{かんこく}や香港{ほんこん}などとの間{あいだ}」
From the context, this means "between (South Korea, Hong Kong and other countries) and Japan". Agreed? This piece of news is about how many tourists Japan receives from other countries.
In other words, this part of the sentence is not talking about what happens between South Korea and Hong Kong.
Remember the double-と rule for formal speech?
「韓国や香港などとの間」
means none other than:
「韓国や香港などと日本との間」
Or, for more visual appeal, it is saying:
「(Some countries) + と + 日本 + と + の + 間」
Hope you enjoyed my "two - と - rial"!
This time, 日本 と 韓国や香港 との間 implies there are relationships between Japan and Korea or Hong Kong as “a partner”.
We don’t talk about what’s going on in the sky between Japan and B this time. It is simply implying there are flights between Japan and South Korea or Hong-Kong.
Using "との" , it is bit strange to imply what a plane is going on in the physical space(e.g. sky) between Japan and Other countries.
It is natural to say "AとBとの間" for a relationship between A and B such as humans, corporations, countries and so on.
Using "の" for a physical line segments such as fence-post at the farm would be better.
Edit1: I think that you can find an exception from my answer.
However, if you say Xの間 or Xとの間, "Xの間" normally treat X as a mass noun. "Xとの間" needs a partner with X.
Goo辞書 https://dictionary.goo.ne.jp/jn/159741/meaning/m0u/%E3%81%A8%E3%81%AE/ also explains
２ …を相手とする。「家族との対話」 ... as a partner. "Conversation with family"
