Cuando pierde el chupete, la niña tiene una rabieta, pero la niñera la calma enseguida.

Because the sentence is describing a typical or repeated situation, not one single past event.

Here, the present tense works like English whenever / every time:

Cuando pierde el chupete, la niña tiene una rabieta...
= When/Whenever she loses her dummy, the girl has a tantrum...

Spanish often uses the present tense for habits, routines, and general truths.

This is a very common question.

After cuando, Spanish uses:

• indicative for something habitual, repeated, or known to happen
• subjunctive for something in the future that has not happened yet

So:

• Cuando pierde el chupete, la niña tiene una rabieta.
  = Whenever she loses her dummy, she has a tantrum.
• Cuando pierda el chupete, la niña tendrá una rabieta.
  = When she loses her dummy, she will have a tantrum.

In your sentence, the speaker is talking about a regular pattern, so pierde is correct.

The subject of pierde is understood to be la niña.

Spanish often leaves out subject pronouns and even subject nouns when the meaning is clear from context. Here, the most natural reading is:

Cuando la niña pierde el chupete...

But Spanish does not need to say la niña in that first clause if it is obvious.

So the sentence could be expanded as:

Cuando la niña pierde el chupete, la niña tiene una rabieta...

That is grammatical, but it sounds repetitive. The original version is more natural.

Spanish often uses the definite article (el, la, los, las) instead of a possessive (mi, tu, su) when the owner is already clear from context.

So:

pierde el chupete
literally = she loses the dummy

But in natural English, we often translate it as:

she loses her dummy

Spanish does this a lot with body parts, clothing, and personal objects when the possessor is obvious.

Using su chupete is possible, but el chupete sounds more natural here.

In Spain, chupete means dummy or pacifier.

A native English speaker should note that this is regional vocabulary. In other Spanish-speaking countries, different words may be more common.

So if you are specifically learning Spanish from Spain, chupete is the normal word to know.

Rabieta means tantrum.

Yes, it is very common in Spain, especially for small children. It refers to the kind of emotional outburst a child has when upset, frustrated, or denied something.

A useful point is that vocabulary can vary by region. In some parts of Latin America, learners may also hear words like berrinche or pataleta, but in Spain rabieta is a very standard choice.

Because tener una rabieta is a normal Spanish expression meaning to have a tantrum.

Spanish often uses tener in places where English may use be, have, or a completely different expression.

So:

la niña tiene una rabieta
means
the girl has a tantrum / throws a tantrum

You may also hear other ways of expressing similar ideas, but tener una rabieta is perfectly natural.

The two la words are doing different jobs.

• la niñera: here la is the definite article, meaning the
• la calma: here la is a direct object pronoun, meaning her

So:

la niñera la calma
= the nanny calms her

The second la refers back to la niña.

Because la is a pronoun.

With a full noun referring to a person, Spanish normally uses the personal a:

La niñera calma a la niña.

But when that object is replaced by a direct object pronoun, you do not use a:

La niñera la calma.

So both mean the same thing:

• La niñera calma a la niña.
• La niñera la calma.

The second version is just using a pronoun instead of repeating the noun.

Here it is a verb.

It comes from calmar, meaning to calm.

So:

la niñera la calma
= the nanny calms her

It only looks like the noun calma because the verb form and the noun are spelled the same. In this sentence, the structure makes it clear that it is the verb.

Enseguida means immediately, right away, or straight away.

So:

la niñera la calma enseguida
= the nanny calms her right away

It is a very common adverb in everyday Spanish.

Because that is a very natural place for it, but Spanish word order is fairly flexible with adverbs.

These are all possible:

• La niñera la calma enseguida.
• La niñera enseguida la calma.
• Enseguida la niñera la calma.

The version in your sentence sounds natural and neutral. Putting enseguida at the end is common when you simply want to add right away as extra information.

In this sentence, it most naturally means whenever she loses it.

That is because the whole sentence is in the present tense and describes a repeated pattern:

• she loses the dummy
• she has a tantrum
• the nanny calms her

So the idea is not one specific event, but a usual sequence of events.

If you wanted to make a single future event clearer, Spanish would usually say something like:

Cuando pierda el chupete, la niña tendrá una rabieta.

Yes, absolutely.

Both are correct:

• pero la niñera la calma enseguida
• pero la niñera calma a la niña enseguida

The version with la sounds more natural in connected speech because Spanish often avoids repeating the noun once it has already been mentioned.

So the original sentence is smoother and more idiomatic.