Al final tuvieron que posponer el viaje por la tormenta, pero mi hermana no perdió la esperanza.

Al final means in the end or at the end. In this sentence, it means in the end / eventually.

It is similar to finalmente, but they are not always identical in tone:

• Al final often sounds more natural in everyday speech when you are talking about the outcome after some process or difficulty.
• Finalmente can also mean finally, but it can sound a little more formal or more like the final step in a sequence.

So here, Al final tuvieron que posponer el viaje feels very natural: In the end, they had to postpone the trip.

Both can mean had to, but they do not feel the same.

• Tuvieron que is preterite. It presents the obligation as a completed event: at that point, they ended up having to postpone it.
• Tenían que is imperfect. It would describe an ongoing situation, background, or repeated obligation.

Here, tuvieron que posponer el viaje shows a specific completed decision or necessity caused by the storm.

Compare:

• Tuvieron que posponer el viaje = they ended up having to postpone the trip
• Tenían que posponer el viaje = they were supposed to / had to postpone the trip, with more of a background or ongoing sense

Tener que + infinitive means to have to do something.

In this sentence:

• tuvieron que = they had to
• posponer = postpone

So:

• tuvieron que posponer = they had to postpone

This is one of the most common ways to express obligation in Spanish.

A few examples:

• Tengo que estudiar = I have to study
• Tenemos que salir = We have to leave
• Tuvo que llamar = He/She had to call

Yes, posponer is a standard verb meaning to postpone or to put off.

It is built like this:

• poner = to put
• posponer = to put later / postpone

It is a useful verb, especially in more neutral or formal contexts. In everyday speech, people also often use:

• aplazar
• dejar para más tarde in some contexts

But posponer el viaje is perfectly natural and very common.

Also, note that posponer is irregular because it follows the pattern of poner in many forms.

Por here expresses cause or reason. So por la tormenta means because of the storm.

This is a very common use of por.

Examples:

• Cancelaron el partido por la lluvia = They cancelled the match because of the rain
• Llegó tarde por el tráfico = He/She arrived late because of traffic

You could also say a causa de la tormenta, but that sounds more formal.
Por la tormenta is the most natural everyday choice.

Spanish often leaves out subject pronouns because the verb ending already shows who the subject is.

• tuvieron tells us the subject is they or you all (depending on context)
• In Spain, here it would normally be understood as they

So Spanish does not need ellos unless the speaker wants emphasis, contrast, or clarity.

Compare:

• Tuvieron que posponer el viaje = They had to postpone the trip
• Ellos tuvieron que posponer el viaje = They had to postpone the trip, with extra emphasis on they

Spanish often uses the definite article where English might not.

Here, el viaje means the trip. It refers to a specific trip already known in the context.

So:

• posponer el viaje = postpone the trip

Spanish generally sounds more natural than English with articles in many expressions like this.

Use pero for a general contrast:

• ..., pero mi hermana no perdió la esperanza = ..., but my sister didn’t lose hope

Use sino after a negative statement when you are correcting it with the true alternative.

For example:

• No fue mi hermano, sino mi hermana = It wasn’t my brother, but rather my sister

In your sentence, the second part is not correcting the first part. It is simply contrasting with it. So pero is the correct conjunction.

Perdió is preterite, and here it means that she did not lose hope as a complete fact.

The sentence presents two completed ideas:

• they had to postpone the trip
• my sister did not lose hope

If you used perdía, it would sound more like an ongoing background description, which does not fit as well here.

So:

• no perdió la esperanza = she didn’t lose hope
• no perdía la esperanza = she wasn’t losing hope / she did not used to lose hope, depending on context

The preterite is more natural in this sentence.

The expression is normally perder la esperanza = to lose hope.

Spanish often uses an article in fixed expressions where English does not.

So the natural phrase is:

• perder la esperanza

Not using the article is much less standard here.

Other similar expressions are:

• tener razón = to be right
• tener miedo = to be afraid
• hacer falta = to be necessary

So it is best to learn perder la esperanza as a whole expression.

Yes, it is very natural. No perder la esperanza is a common expression meaning not to lose hope.

It is a standard, idiomatic way to speak in Spanish.

You could also hear:

• mi hermana siguió teniendo esperanza
• mi hermana siguió siendo optimista
• mi hermana no dejó de tener esperanza

But no perdió la esperanza is the most direct and idiomatic version.

No. Hermana just means sister.

If you want to specify, you would say:

• hermana mayor = older sister
• hermana menor = younger sister

So mi hermana simply means my sister.

The sentence breaks down like this:

• Al final = in the end
• tuvieron que posponer el viaje = they had to postpone the trip
• por la tormenta = because of the storm
• pero = but
• mi hermana no perdió la esperanza = my sister did not lose hope

So the structure is basically:

time/result expression + main clause + cause + contrast + second clause

This is a very common and natural sentence pattern in Spanish.