Demà vaig a l'estació amb la meva filla, i després venim a casa.

That is a very common source of confusion.

In this sentence, vaig is the present tense of anar:

• jo vaig = I go / I am going

But vaig also appears in the periphrastic past:

• vaig anar = I went

So:

• vaig by itself can mean I go
• vaig + infinitive can form a past meaning, like vaig veure = I saw

Here, because we have Demà (tomorrow), vaig is understood as present with future meaning: Tomorrow I’m going...

Catalan, like English, often uses the present tense to talk about planned or scheduled future actions.

So Demà vaig a l'estació is very natural, just like English Tomorrow I’m going to the station.

You could also use the future:

• Demà aniré a l'estació

That is also correct, but the present often sounds more immediate or more like a plan.

Because the subject changes.

• vaig = I go
• venim = we come

So the idea is:

• first, I go to the station with my daughter
• then, we come home

The second verb is plural because after that point, the speaker and the daughter are acting together.

Catalan usually drops subject pronouns when the verb ending already shows who the subject is.

For example:

• vaig already tells you it is I
• venim already tells you it is we

So jo vaig and nosaltres venim are possible, but they are usually only used for emphasis, contrast, or clarity.

Because the feminine article la becomes l' before a vowel sound.

So:

• la estació becomes l'estació

After the preposition a, you get:

• a l'estació = to the station

This is an elision, used to make pronunciation smoother.

In Catalan, possessives are very often used with the definite article.

So:

• la meva filla = my daughter
• literally, something like the my daughter, though you should not translate it word-for-word

This is especially common with family words and everyday nouns.

So amb la meva filla is the normal way to say with my daughter.

Because a casa is a fixed, very common expression meaning home or to/at home.

So:

• anar a casa = to go home
• ser a casa = to be at home
• venir a casa = to come home / come to the house

If you said a la casa, that would usually mean to the house, referring to a particular building rather than home in the usual sense.

All three verbs can make sense, but they are not exactly the same.

• venir a casa = come home / come to the house
• anar a casa = go home
• tornar a casa = return home

In Catalan, venir is often used when the movement is toward the speaker’s home or usual place. Since casa is the speaker’s home, venim a casa works naturally.

That said, tornem a casa would also be very common if you want to emphasize returning home.

Here després is being used as an adverb, meaning afterwards / then / later.

So:

• i després venim a casa = and afterwards we come home

You use després de when something follows it:

• després de dinar = after lunch
• després de treballar = after working

But when després stands alone, you do not need de.

The given word order is natural.

• Demà vaig a l'estació...

Starting with Demà is very normal because it sets the time frame right away.

You could move things around in some contexts, but Vaig demà a l'estació is much less natural in neutral speech. Catalan usually prefers the time expression either at the beginning or later in a more natural rhythm, such as:

• Demà vaig a l'estació
• Vaig a l'estació demà

The first version is especially common.

It is not always necessary.

In Catalan, a comma before i is often omitted, especially in simple sentences. So this would also be perfectly fine:

• Demà vaig a l'estació amb la meva filla i després venim a casa.

The comma can be used to mark a pause or to separate two clauses more clearly, especially when the subject or action changes. Here, the sentence moves from I go to we come, so the comma is understandable, but it is not mandatory.

Yes. Amb is the standard Catalan preposition for with.

So:

• amb la meva filla = with my daughter

It is used for accompaniment, instrument, and other common meanings of with.

Examples:

• amb un amic = with a friend
• amb un ganivet = with a knife

So in this sentence it simply shows that the speaker goes to the station together with the daughter.