Ŝi diris, ke post longa tago ŝi plej volas sidi trankvile, legi poemon kaj ne plu stiri inter bruaj veturiloj.

Ke means that and introduces a subordinate clause.

So Ŝi diris, ke... means She said that...

This is very common in Esperanto after verbs like:

• diri = to say
• pensi = to think
• scii = to know
• kredi = to believe

So the sentence is structured as:

• main clause: Ŝi diris
• subordinate clause: ke post longa tago ŝi plej volas...

Because the subordinate clause needs its own subject.

In English, learners sometimes feel the second she is unnecessary because the subject is already clear from She said. But in Esperanto, it is normal and clear to state the subject again:

• Ŝi diris, ke ŝi volas ripozi. = She said that she wants to rest.

Without the second ŝi, the clause would feel incomplete.

Post is a preposition meaning after.

So:

• post = after
• longa = long
• tago = day

Together, post longa tago means after a long day.

A few grammar points:

• longa ends in -a because it is an adjective.
• It describes tago, so it agrees with it.
• There is no -n here, because post is a preposition, and prepositions normally take a noun without -n unless motion/direction is being emphasized.

Plej means most.

Here it modifies volas, so ŝi plej volas... means:

• she wants most to...
• or more naturally in English, what she wants most is to...

This is a very normal Esperanto way to say above all, she wants to...

Compare:

• Mi volas dormi. = I want to sleep.
• Mi plej volas dormi. = What I want most is to sleep.

Because they depend on volas.

After voli (to want), Esperanto normally uses an infinitive for the action wanted:

• Mi volas manĝi. = I want to eat.
• Ŝi volas legi. = She wants to read.

So in your sentence, she wants:

• sidi trankvile = to sit quietly
• legi poemon = to read a poem
• ne plu stiri inter bruaj veturiloj = to no longer drive among noisy vehicles

All three infinitives are governed by the one verb volas.

Because trankvile is an adverb, and it modifies the verb sidi.

• trankvila = calm, quiet, peaceful (adjective)
• trankvile = calmly, quietly, peacefully (adverb)

Here the meaning is to sit quietly/calmly, so you need the adverb:

• sidi trankvile

If you used trankvila, it would need to describe a noun, for example:

• trankvila virino = a calm woman

Because it is the direct object of legi.

In Esperanto, the direct object usually takes -n:

• Mi legas libron. = I read a book.
• Ŝi legi poemon would be wrong in normal Esperanto.
• Ŝi volas legi poemon. = She wants to read a poem.

So:

• poemo = poem
• poemon = a poem, as the thing being read

Ne plu means no longer or not anymore.

So:

• ne plu stiri = to no longer drive / to not drive anymore

This is a very common expression in Esperanto.

Examples:

• Mi ne plu fumas. = I no longer smoke.
• Ili ne plu loĝas tie. = They no longer live there.

By itself, plu often has the idea of further / more / any longer, especially in negative contexts.

Because after a preposition, Esperanto normally uses the noun without -n.

Here:

• inter = among / between
• bruaj veturiloj = noisy vehicles

So inter bruaj veturiloj means among noisy vehicles.

The accusative -n after a preposition is mainly used when you want to show direction or movement toward a place. But here the idea is not into a place between vehicles. It is simply the setting in which she is driving: among noisy vehicles.

So the normal form here is:

• inter bruaj veturiloj

Because it describes veturiloj, which is plural.

• veturilo = vehicle
• veturiloj = vehicles
• bruaj veturiloj = noisy vehicles

In Esperanto, adjectives agree with the nouns they describe in number and case:

• singular noun -> singular adjective
• plural noun -> plural adjective
• accusative noun -> accusative adjective too

So:

• brua veturilo = a noisy vehicle
• bruaj veturiloj = noisy vehicles

Yes. Stiri can mean to steer or to drive/control a vehicle, depending on context.

In this sentence, stiri inter bruaj veturiloj is naturally understood as to drive among noisy vehicles.

So although the core idea of stiri is controlling direction, in many contexts it works just like English drive.

The comma before ke marks the start of a subordinate clause:

• Ŝi diris, ke...

That is very common and standard in Esperanto writing.

The commas in the middle help separate items in a list of infinitives:

• sidi trankvile
• legi poemon
• kaj ne plu stiri inter bruaj veturiloj

So the punctuation makes the structure clearer: she said that, after a long day, what she wants most is:

1. to sit quietly,
2. to read a poem,
3. and to no longer drive among noisy vehicles.

Yes, but the meaning would change slightly.

• Ŝi volas sidi trankvile, legi poemon kaj ne plu stiri... = She wants to sit quietly, read a poem, and no longer drive...

• Ŝi plej volas sidi trankvile, legi poemon kaj ne plu stiri... = What she wants most is to sit quietly, read a poem, and no longer drive...

So plej adds emphasis. It tells you this is her strongest wish after that long day.