Me alegra que mis hijas quieran adoptar una mascota, siempre que la cuiden bien.

Literally, me alegra means it makes me happy or it pleases me.

Spanish often uses alegrar this way:

• Algo me alegra = Something makes me happy
• Me alegra que... = I’m glad that... / It makes me happy that...

So in this sentence, the whole clause que mis hijas quieran adoptar una mascota... is the thing that makes me happy.

Because que introduces the subordinate clause: the part that explains what makes the speaker happy.

Structure:

• Me alegra
  • que
    • clause

So:

• Me alegra que mis hijas quieran adoptar una mascota
  = I’m glad that my daughters want to adopt a pet

This is a very common Spanish pattern after expressions of emotion, opinion, or reaction.

Because after me alegra que, Spanish normally uses the subjunctive.

The sentence expresses an emotion about what someone else does or wants, and that triggers the subjunctive:

• Me alegra que mis hijas quieran...

Here:

• quieran = present subjunctive
• quieren = present indicative

So quieren would sound wrong in standard Spanish in this sentence.

Quieran is the present subjunctive, third person plural, of querer.

Why third person plural? Because the subject is mis hijas = my daughters.

So:

• yo quiera
• tú quieras
• él/ella quiera
• ellos/ellas quieran

Since mis hijas = ellas, the correct form is quieran.

Because after querer, the next verb stays in the infinitive.

This is the same idea as in English:

• They want to adopt
• Quieren adoptar

So in:

• mis hijas quieran adoptar una mascota

quieran is the conjugated verb, and adoptar stays unconjugated.

Here, siempre que means as long as or provided that.

So:

• siempre que la cuiden bien = as long as they take good care of it

Although siempre often means always, the phrase siempre que has a special meaning depending on context:

• whenever
• as long as
• provided that

In this sentence, it clearly means a condition: the speaker is glad about it only if they take good care of the pet.

Because siempre que can take the subjunctive when it introduces a condition that has not yet been confirmed as true.

Here the idea is:

• I’m glad they want to adopt a pet, provided that they take good care of it

That is a condition, not a stated fact, so Spanish uses:

• cuiden = present subjunctive

If you said cuidan, it would sound more like a habitual or factual meaning:

• whenever they take good care of it

But in this sentence, the meaning is conditional, so cuiden is the natural choice.

La refers to una mascota.

So:

• una mascota = a pet
• la cuiden bien = they take good care of it

Spanish often replaces a previously mentioned direct object with a pronoun:

• una mascota → la

That avoids repeating the noun.

Because la refers to the pet, not to the daughters.

There are two different things happening:

• mis hijas is the subject of quieran and cuiden, so the verbs are plural
• la is the direct object pronoun referring to una mascota, which is singular

So:

• mis hijas → plural subject → quieran, cuiden
• una mascota → singular object → la

In standard spelling, it would be cuidenla only if it were allowed as an attached pronoun form, but with a fully conjugated finite verb like cuiden, object pronouns normally go before the verb:

• la cuiden

Spanish attaches pronouns to:

• infinitives: cuidarla
• gerunds: cuidándola
• affirmative commands: cuídenla

But with a normal conjugated verb in a clause, the pronoun goes before:

• que la cuiden bien

Not necessarily. Mascota is a grammatically feminine noun, so it takes:

• una mascota
• la mascota

But that does not always mean the animal is biologically female.

Spanish grammatical gender and real-life sex are not always the same thing. So la mascota can refer to a male pet or a female pet.

That is why the pronoun is la:

• una mascota → la

Yes. Both are correct and very common.

• Me alegra que... = It makes me happy that...
• Me alegro de que... = I’m glad that...

They are very close in meaning.
A small difference in feel:

• Me alegra que... can sound a bit more like a reaction to a situation
• Me alegro de que... can sound a bit more directly personal

But in everyday use, both are natural.

Because una mascota is the direct object of adoptar, and the personal a is mainly used with specific human direct objects.

Compare:

• Veo a mi hermana = I see my sister
• Quiero adoptar una mascota = I want to adopt a pet

Since una mascota is:

• not human
• indefinite
• not a specific named pet

there is no a here.

With animals, Spanish sometimes does use a if the animal is specific or treated very personally, but in this sentence una mascota is general, so no a is needed.

Yes, the meaning would shift.

• siempre que la cuiden bien
  = as long as they take good care of it / provided that they take good care of it

This is conditional and uses the subjunctive.

• siempre que la cuidan bien
  would suggest something more like whenever they take good care of it, which sounds more habitual or factual

So the sentence as written is expressing a condition, not a repeated fact.

Because the plural possessive mis is the same for both genders.

Compare:

• mi hija = my daughter
• mi hijo = my son
• mis hijas = my daughters
• mis hijos = my sons

So mis only shows:

• possessor: my
• number: plural noun

It does not change for masculine vs feminine in the plural form.