... うちに, ... ”うちに” is USUALLY used in vague time frame.

走っていたときに, 有名な歌手を見ました. ← You know exactly when you saw the famous singer.

駅で待っているあいだに, 試験のじゅんびをしていました. ← This is not vague time frame because I can imagine in what time frame you were studying for the test.

台所で料理（を）していると, 主人が家に帰ってきました. ←Same as the first one.

旅館に泊まってるあいだに, 生け花を習いました. ←Same as the second one. You can use "うちに" if the sentence was "旅館に泊まっているうちに生け花を習いたい" because you haven't decide exactly when but sometime while you are staying at the hotel.

森を歩いているうちに、 病気になりました.←You can use "うちに" here because I am not sure exactly when and how long you were sick.

This is a very confusing grammar point...

While I was running, I  saw a famous singer
While I waited at the station, I prepared for an exam
While I was cooking in the kitchen, my husband returned home.
While I stayed at the hotel, I learned flower arranging.
As I walked round the forest, I became sick.