According to the book I'm reading, both of these sentences translate to: “I bought a bag when I went back to my country”.
Now the nuance, if I understand correctly, is that
Is my understanding correct?
I'm Japanese. I hope to improve my English and use English more often, so I'll answer your question.
As Darius-san wrote, 2 is ambiguous, and most Japanese think that she arrived in her country and then bought the bag. But if I translate these sentences without thinking well, I might do both to "I bought a bag when I went back to my country." Given this, I come to think that this English sentence is also ambiguous. When do you think the speaker bought a bag?
By the way, the sentence "国へ帰る時、かばんを買いました。でもやっぱり帰りませんでした" Darius-san wrote is pretty strange. Japanese never say so.
If you say this, it is correct:
国に帰るためにかばんを買いました。でも、やっぱり帰りませんでした。
I bought a bag to return to my country. But it turns out that I never actually got home.
Your first sentence necessarily implies that she got home.
My English may prevent you from understanding. Sorry.
I do not think the nuance you listed gives the full picture.
国へ帰るとき、かばんを買いました。
This can be said if you bought the bag before you returned (i.e., on the airplane, in the departure airport, etc.).
国へ帰ったとき、かばんを買いました。
This can be said if you bought the bag before you returned, or when you completed returning.
So, the natural reading of the second sentence is probably that the bag was bought when you returned, but it's rather ambiguous and could easily mean before you returned.
There is a more important difference between the sentences though, which is that the former sentence does not necessarily imply that you got home:
国へ帰る時、かばんを買いました。でもやっぱり帰りませんでした。
"When I was returning to my country, I bought a bag. But, it turns out that I never actually got home."国へ帰った時、かばんを買いました。でもやっぱり帰りませんでした。
Semantically invalid, 帰った conflicts with 帰りませんでした.
As mentioned, your first sentence does not necessarily imply that you got home, which is why you can add でもやっぱり帰りませんでした.
Note, that behavior of the plain form in relative clauses only works like that for a state-change verb (e.g., 帰る), not for action verbs (e.g., 走る).
道を（毎日）走る時、宇宙人を見たことがありました。 "Back when I was running the streets (every day), I saw an alien."
When your embedded verb (走る) is an action verb in plain form, if the matrix predicate (ある) is past-tense, the embedded verb is forced to take on a habitual reading.
In this case adding でもやっぱり走りませんでした, "but I never ran" does not make sense semantically.
