Dóttir mín er glöð þegar amma kemur.

Both are possible, but dóttir mín is the more neutral and natural order here.

In Icelandic, possessive words like mín often come after the noun, especially in everyday language and especially with family words and familiar relationships.

• dóttir mín = the normal way to say my daughter
• mín dóttir = more emphatic, contrastive, or stylistically marked, like my daughter as opposed to someone else’s

So in an ordinary statement, dóttir mín is what you would usually expect.

Because a possessive already makes the noun definite in meaning.

Dóttir mín already means my daughter, which is definite enough by itself. Icelandic usually does not add the definite article when a noun has a possessive.

So:

• dóttir mín = normal, natural
• dóttirin mín = possible, but more marked and usually used for special emphasis or a very specific discourse context

This is similar to how English says my daughter, not the my daughter.

The important noun forms here are in the nominative case.

• dóttir is nominative because it is the subject of er glöð
• amma is nominative because it is the subject of kemur

Also:

• mín matches dóttir, so it is also feminine singular nominative
• glöð matches the subject too, so it is feminine singular nominative as well

So the sentence is a good example of how Icelandic keeps agreement visible in several words at once.

Because glöð is the form that agrees with a feminine singular subject.

The dictionary form of the adjective is glaður meaning glad/happy, but adjectives change form in Icelandic depending on gender, number, and case.

Here the subject is dóttir mín, and dóttir is feminine singular, so the adjective must match:

• masculine: glaður
• feminine: glöð
• neuter: glatt

So:

• Dóttir mín er glöð
• but Sonur minn er glaður

Yes. Possessive words like minn meaning my also decline.

Here it appears as mín because it must agree with dóttir, which is feminine singular nominative.

Compare:

• sonur minn = my son
• dóttir mín = my daughter
• barn mitt = my child

So minn / mín / mitt work a lot like adjectives in that they change form to match the noun.

Here þegar means when.

It introduces a time clause:

• þegar amma kemur = when grandma comes

In other contexts, þegar can sometimes have a broader sense like whenever, depending on the sentence, but in this example the straightforward meaning is just when.

Because this is a subordinate clause introduced by þegar.

In a main clause, Icelandic often follows the verb-second pattern, but subordinate clauses usually have more straightforward order, often:

conjunction + subject + verb

So here:

• þegar = conjunction
• amma = subject
• kemur = verb

That gives:

• þegar amma kemur

This is normal and expected.

Kemur is the 3rd person singular present tense of the verb koma meaning to come.

So:

• ég kem = I come
• þú kemur = you come
• hann/hún/það kemur = he/she/it comes

Since amma is a singular third-person subject, kemur is the correct form.

This verb is not fully regular, because the vowel changes from o in koma to e in some present-tense forms.

Yes. You can also say:

Þegar amma kemur er dóttir mín glöð.

That is perfectly natural.

When the subordinate clause comes first, the main clause still keeps normal Icelandic clause structure, with the finite verb early in the clause:

• Þegar amma kemur er dóttir mín glöð

So both orders are possible:

• Dóttir mín er glöð þegar amma kemur
• Þegar amma kemur er dóttir mín glöð

The difference is mainly one of emphasis and information flow, not basic meaning.

It is closer in feeling to grandma, but English labels do not match perfectly.

Amma is the normal everyday Icelandic word people use for their grandmother. It is warm and common, and not unusually childish. In many situations it is simply the standard word you would use.

So if you translate it as grandma, that usually gives the right tone better than the more formal-sounding grandmother.

Because it is being used as a common noun here, not as a name.

In this sentence, amma means grandma/grandmother in a general family-role sense, so it stays lowercase:

• amma kemur

If it were being used directly as a name in some English-style contexts, capitalization might happen in English, but Icelandic normally keeps nouns like this lowercase unless they begin the sentence.

Not in this sentence.

Modern Icelandic usually does not require a comma before a short subordinate clause like þegar amma kemur, so the sentence as written is normal:

Dóttir mín er glöð þegar amma kemur.

You may sometimes see commas used in longer or more complex sentences, but here no comma is needed.