haha wo eki made miokuri ni itta ato, watasi ha sonomama tosyokan ni yorimasita.

Because 見送りに行く is a set pattern:

• Vます-stem + に行く = go in order to do V

So:

• 見送る = to see someone off
• 見送り = the ます-stem of 見送る
• 見送りに行った = went to see someone off

This is the same pattern as:

• 買いに行く = go to buy
• 食べに行く = go to eat
• 迎えに行く = go to pick someone up

So 見送りに行った does not mean “went and did something called a send-off” in a literal noun sense; it is the normal grammar for go to do X.

It breaks down like this:

• 母を = mother (as the object)
• 駅まで = as far as the station / to the station
• 見送りに行った = went to see her off

So the structure is basically:

• [person] を [place] まで 見送る = see [person] off as far as [place]

Then that whole action becomes:

• 母を駅まで見送りに行った = went to see my mother off to the station

The important point is that 母 is the person being seen off, and 駅まで is the destination up to which the speaker accompanied her.

Because 見送る takes a direct object.

• 母を見送る = see mother off

Here, the mother is the person being accompanied/sent off, so she is marked with を.

Even though English may phrase this differently, in Japanese the person being seen off is treated as the object of 見送る.

まで means up to, as far as, or until.

So:

• 駅まで見送る = see someone off as far as the station

This emphasizes the endpoint of the accompaniment.

If you said 駅に or 駅へ, it would focus more simply on direction or destination. But with 見送る, まで is very natural because the idea is “go with someone up to a certain place and part from them there.”

So 駅まで fits the meaning very well.

Because 行った is inside the grammar pattern Vた + あと:

• 行ったあと = after going

Before あと, Japanese normally uses the plain past form.

The final verb of the sentence, however, is the main predicate:

• 寄りました

That is where the speaker shows politeness.

So this is completely normal:

• subordinate clause: plain form
• main sentence ending: polite form

You often see this kind of mix in Japanese.

あと means after.

The pattern is:

• Vた + あと = after doing V

So:

• 行ったあと = after going

In this sentence, it means that the action of going to see the mother off happened first, and then the next action happened:

1. went to see mother off to the station
2. after that, stopped by the library

This is one of the most common ways to say after doing something in Japanese.

Yes, most naturally it is the speaker, even though the subject is omitted.

Japanese often leaves out the subject when it is understood from context. In this sentence:

• 母を駅まで見送りに行ったあと、私は…

the first clause has no explicit subject, but the second clause says 私は, so the natural reading is that the same person did both actions.

So the implied subject of 見送りに行った is also I.

そのまま means something like:

• just like that
• without changing anything
• straight from there
• without going home or stopping for something else first

In this sentence, it means the speaker went to the library directly after seeing their mother off, without any real break or change of course.

So the nuance is:

• “After I went to see my mother off at the station, I then went straight to the library.”

Not exactly.

寄る means:

• to stop by
• to drop in
• to call at somewhere briefly, often on the way to or from somewhere else

So:

• 図書館に寄りました = I stopped by the library

This gives a different nuance from simply 図書館に行きました:

• 行きました = went to the library
• 寄りました = stopped by the library, likely as an extra stop

Because the sentence also has そのまま, 寄りました feels very natural: the speaker finished one errand and then dropped by the library on the way.

Because 寄る often uses に to mark the place where someone stops by.

• コンビニに寄る = stop by the convenience store
• 友だちの家に寄る = stop by a friend’s house
• 図書館に寄る = stop by the library

So here に marks the destination/place of the stop.

Japanese often introduces or highlights the topic only where it is useful.

In the first clause, the subject is easy to understand from context, so it is omitted:

• 母を駅まで見送りに行ったあと

Then in the second clause, 私は appears to set up the main statement clearly:

• 私はそのまま図書館に寄りました

This can sound very natural because the first part is background information, and the second part is the main point.

Yes, and it would mean something slightly different.

• 母を駅まで見送ったあと = after seeing my mother off to the station
• 母を駅まで見送りに行ったあと = after going to see my mother off to the station

The version in your sentence includes 行った, which makes the “went to do that” idea explicit. It suggests that the speaker went somewhere for the purpose of seeing their mother off.

Without 行った, the sentence focuses more simply on the completed action of seeing her off.

Both are natural, but they are not exactly identical in nuance.

In this kind of sentence, 母 normally means my mother.

Japanese often uses family terms like:

• 母 = my mother
• 父 = my father

when talking about one’s own family to other people.

So even though there is no word like my, the natural interpretation is my mother.