Ég rugla henni stundum saman við systur hennar.

It is a fixed expression meaning to mix someone/something up with someone/something else or to mistake X for Y.

So in this sentence:

• Ég = I
• rugla henni saman við systur hennar = mix her up with her sister

A very literal breakdown would be something like confuse her together with her sister, but that is not how it is understood in real Icelandic. You should learn rugla ... saman við as one pattern.

Because this construction uses the first person/thing being confused in the dative.

So here:

• henni = dative of hún
• it refers to the person I mistake for someone else

This is something you largely have to learn with the expression itself:

• rugla e-u saman við e-ð = mix up X with Y

That is worth remembering as a chunk.
Also, this does not mean that rugla always takes dative in every use. In other contexts, rugla can behave differently.

Because after við in this expression, the noun is in the accusative.

The dictionary form is:

• systir = sister

But here you need the accusative singular:

• systur

So:

• við systur hennar = with / for her sister in the sense of mistaking someone for her sister

A useful point: systur can be more than one case form in Icelandic, but here it is accusative because of við.

They are different forms of the pronoun hún.

Here are the most important forms:

• hún = she
• hana = her (accusative)
• henni = her (dative)
• hennar = her / hers (genitive, often possessive)

In this sentence:

• henni = her as the person being mixed up with someone else
• hennar = her in the sense of her sister

So the two words are related, but they do different grammatical jobs.

Because sinn is a reflexive possessive that points back to the subject, and that does not fit here.

The subject of the sentence is:

• Ég = I

But the sister belongs to her, not to me. So the correct possessive is:

• systur hennar = her sister

If you used sinnar, you would be invoking the reflexive system, which is not what this sentence needs.

Stundum means sometimes.

It tells you how often the action happens:

• Ég rugla henni stundum saman við systur hennar.
• I sometimes mix her up with her sister.

So it is just an adverb of frequency.

Yes, it can move, but the placement here is very natural.

In this sentence, henni is a short unstressed pronoun, and Icelandic often places such pronouns fairly early in the sentence. That is why henni comes before stundum.

You can also front stundum for emphasis:

• Stundum rugla ég henni saman við systur hennar.

That still means the same thing, just with a different emphasis: Sometimes, I mix her up with her sister.

Because Icelandic main clauses normally follow the verb-second rule.

That means the finite verb usually comes in the second slot of the clause.

Here:

• first slot: Ég
• second slot: rugla

So the sentence starts:

• Ég rugla ...

If you put something else first, the verb still stays second:

• Stundum rugla ég henni saman við systur hennar.

This verb-second pattern is one of the most important word-order rules in Icelandic.

Yes, saman often means together, but in this sentence it is part of the fixed expression rugla ... saman við.

So even though saman has a literal meaning of together, you should not translate the sentence word-for-word. Here the whole combination means:

• mix up
• mistake one person for another

So saman is not adding a separate idea of physical togetherness here; it is helping form the idiomatic meaning.