Amma ruggar henni varlega í rimlarúminu þegar hún grætur.

Because the verb rugga takes its object in the dative case, not the accusative.

• hún = she
• hana = her (accusative)
• henni = her (dative)

So in Amma ruggar henni..., the baby is the object of ruggar, and this verb requires dative, so henni is correct.

This is something you just have to learn with certain Icelandic verbs: not all direct objects are accusative.

Ruggar is the present tense of rugga, meaning to rock or to gently sway.

So Amma ruggar henni means Grandma rocks her.

The form ruggar is:

• 3rd person singular
• present tense

That fits Amma = she.

Varlega is an adverb, meaning gently, carefully, or softly.

It describes how Grandma rocks her:

• Amma ruggar henni varlega = Grandma rocks her gently

It comes from the adjective varlegur = careful / gentle, but here it is in adverb form, so it modifies the verb ruggar.

Í rimlarúminu means in the crib.

Breakdown:

• rimlarúm = crib, cot
• í = in
• rimlarúminu = the crib

The ending -inu / -nu shows:

1. the noun is definite = the crib
2. it is in the dative singular

That happens because í takes:

• dative when it means location: in
• accusative when it means motion into

Here the meaning is location: Grandma is rocking her in the crib, so dative is used:

• í rimlarúminu

Because this sentence describes where the action happens, not movement into the crib.

Compare:

• í rimlarúminu = in the crib → location, so dative
• inn í rimlarúmið = into the crib → movement/direction, so accusative

In your sentence, the baby is already in the crib, and Grandma is rocking her there, so í rimlarúminu is the natural choice.

Literally it means when she cries.

Breakdown:

• þegar = when
• hún = she
• grætur = cries / is crying

In natural English, depending on context, it could be understood as:

• when she cries
• when she is crying

Icelandic often uses the simple present in places where English might choose either simple present or progressive.

Most likely it refers to the baby, not Grandma.

So the meaning is:

• Grandma rocks her gently in the crib when she cries

Grammatically, hún could in theory refer to any feminine singular person already mentioned, but context makes the baby the natural interpretation. Grandma rocking the baby when Grandma cries would be possible grammatically, but it is not the intended reading.

This kind of pronoun ambiguity can happen in Icelandic just as it can in English.

Yes. The present tense here can describe a habitual or general action.

So the sentence suggests something like:

• Grandma rocks her gently in the crib when she cries
• meaning this is what Grandma typically does whenever the baby cries

It does not have to mean the action is happening right now. Icelandic present tense often works this way, just like English simple present in habitual statements.

Yes, this is very normal Icelandic word order.

Main clause:

• Amma = subject
• ruggar = verb
• henni = object
• varlega = adverb
• í rimlarúminu = prepositional phrase

Then the subordinate clause:

• þegar hún grætur = when she cries

So the structure is basically: Subject + Verb + Object + Adverb + Place + Time clause

That is a very natural neutral order in Icelandic.

Yes. You could also say:

Þegar hún grætur, ruggar amma henni varlega í rimlarúminu.

That means the same thing: When she cries, Grandma rocks her gently in the crib.

When a subordinate clause comes first in Icelandic, the main clause usually follows normal verb-second order, so the verb comes before the subject:

• Þegar hún grætur, ruggar amma...

Not:

• Þegar hún grætur, amma ruggar...

Because Amma here means Grandma as a family role or form of address, not the grandmother as a noun phrase.

In English we also often say:

• Grandma rocks her gently...

not:

• The Grandma rocks her gently...

If you wanted to say the grandmother, Icelandic would more likely use:

• Amman = the grandmother

But Amma here functions more like a family title: Grandma.

Yes, rimlarúm is a normal word for a crib or cot.

It is a compound:

• rimlar = bars / slats
• rúm = bed

So literally it is something like bar-bed or slatted bed, which makes sense for a crib with rails.

Compound nouns are extremely common in Icelandic, so learners should get used to spotting them.

It is dative singular definite.

Here is the breakdown:

• base noun: rimlarúm
• definite form: rimlarúmið = the crib
• after í with location, it becomes dative:
  • í rimlarúminu = in the crib

So this one word tells you:

• singular
• definite
• dative

That is a very typical Icelandic pattern.