Quan arribi la meva mare, la vull abraçar.

Because after quan when you are talking about a future event that has not happened yet, Catalan normally uses the present subjunctive:

Quan arribi la meva mare... = When my mother arrives...

This is different from English, which also avoids will in this kind of clause, but uses the present simple instead. In Catalan:

• Quan arribi... = future, not yet happened
• Quan arriba... = habitual or general meaning, like whenever she arrives
• Quan arribarà... is generally not the normal choice here

So arribi is the expected form in this sentence.

Arribi is the present subjunctive form of arribar.

For this verb, the relevant forms are:

• jo arribi
• ell/ella/vostè arribi

So the form itself could be I arrive or she arrives in the subjunctive, but here the subject is la meva mare, so it clearly means she arrives.

No. It depends on the meaning.

Use the subjunctive after quan when the action is in the future or not yet realized:

• Quan arribi la meva mare, la vull abraçar.

Use the indicative when you are talking about something habitual, repeated, or already factual:

• Quan arriba la meva mare, sempre fem cafè.
  = Whenever my mother arrives, we always have coffee.

• Quan va arribar la meva mare, la vaig abraçar.
  = When my mother arrived, I hugged her.

So it is not quan by itself that causes the subjunctive; it is the future/unrealized meaning.

La is a direct object pronoun meaning her.

It refers back to la meva mare. So:

• la vull abraçar = I want to hug her

Catalan often uses these short object pronouns, called weak pronouns or clitics, instead of repeating the noun.

You could also say:

• Quan arribi la meva mare, vull abraçar la meva mare.

But that sounds repetitive, so la is the natural choice.

Yes. Both are correct:

• la vull abraçar
• vull abraçar-la

With a conjugated verb plus an infinitive, Catalan often allows the object pronoun in either place:

• before the conjugated verb: la vull abraçar
• attached to the infinitive: vull abraçar-la

Both mean the same thing. The first one is very common and natural; the second is also perfectly normal.

What you cannot say is:

• vull-la abraçar ❌

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

• la meva mare
• el meu pare
• la teva germana

This is normal Catalan grammar, especially with family members. English does not do this, so it feels unusual to English speakers at first.

So la meva mare is the standard way to say my mother.

Catalan often leaves out subject pronouns because the verb ending already shows the person.

Here, vull means I want, so jo is not necessary.

• la vull abraçar = I want to hug her
• jo la vull abraçar = also correct, but jo adds emphasis

Catalan is a pro-drop language, unlike English.

In standard Catalan, normally:

• abraçar la meva mare

Catalan usually does not use a personal a before a direct object the way Spanish often does.

So for learners, the safe rule is:

• Vull abraçar la meva mare. ✅
• Vull abraçar a la meva mare. usually not standard

There are some dialectal or special cases, but in ordinary standard Catalan, omit the a here.

Yes. Both are correct:

• Quan arribi la meva mare...
• Quan la meva mare arribi...

Catalan allows both subject positions. The subject often comes after the verb quite naturally, especially in subordinate clauses, but putting it before the verb is also completely fine.

So this is mostly a matter of style and rhythm, not a change in meaning.

Yes, it is the normal choice in writing.

The first part, Quan arribi la meva mare, is an introductory subordinate clause. In Catalan, as in English, it is standard to separate that from the main clause with a comma:

• Quan arribi la meva mare, la vull abraçar.

In very informal writing, people sometimes leave commas out, but the version with the comma is the correct and recommended one.