Learn Hardcore Danish: Lad os i stedet for at skændes tale roligt om problemet. - Instead of arguing, let’s talk calmly about the problem.

So Lad os tale … is literally “Let us talk …”, but idiomatically it just means “Let’s talk …”.
You use Lad os + infinitive to suggest something you and the listener should do together:

Lad os gå hjem. – Let’s go home.
Lad os spise. – Let’s eat.

Why is it os and not vi after Lad?

In Danish, os is the object form of vi (we), just like us is the object form of we in English.

Because the literal structure is “let us do X”, Danish (like English) uses the object form:

English: Let *us talk.*
Danish: Lad os tale.

You would not say Lad vi tale, just like you don’t say Let we talk in English.

Why does tale come so late in the sentence, after i stedet for at skændes?

The structure is:

Lad os – “let’s”
i stedet for at skændes – “instead of arguing” (an adverbial phrase)
tale roligt om problemet – “talk calmly about the problem”

In Danish, the finite verb has to be in second position (V2 word order). Here the finite verb is Lad, so that requirement is already satisfied. The verb tale is an infinitive, so it doesn’t have to be second; it can come later, after the whole i stedet for at skændes phrase.

This is a very natural pattern: a long adverbial phrase (i stedet for at skændes) can be placed before the main infinitive tale:

Lad os i stedet for at skændes tale roligt om problemet.

You could also say:

Lad os i stedet tale roligt om problemet, i stedet for at skændes.

Both are grammatical; they just arrange the “instead of arguing” idea differently in the sentence.

What does i stedet for mean, and is it different from i stedet?

i stedet means “instead”.
i stedet for means “instead of”, and is normally followed by a noun or an infinitive with at.

In this sentence we need “instead of arguing”, so we must use i stedet for:

i stedet for at skændes – instead of arguing

Other examples:

Vi tager bussen i stedet. – We’ll take the bus instead.
Vi tager bussen i stedet for toget. – We’ll take the bus instead of the train.
I stedet for at klage, burde du gøre noget. – Instead of complaining, you should do something.

Why do we need at in i stedet for at skændes?

In Danish, at is the normal infinitive marker, like to in English:

at tale – to talk
at spise – to eat
at skændes – to argue

After i stedet for, when you follow it with a verb, you use at + infinitive:

i stedet for at skændes – instead of arguing
i stedet for at råbe – instead of shouting
i stedet for at græde – instead of crying

So at here just shows that skændes is an infinitive.

What kind of verb is skændes, and why does it end in -s?

skændes is a so‑called “-s-verb” (mediopassive/reflexive type). The basic verb is at skændes, and it already includes the idea of “with each other / with someone”:

at skændes – to argue (often “argue with each other”)

You don’t normally say at skænde in the sense of “argue”; skændes is the standard form.

Examples:

De skændes hele tiden. – They argue all the time.
Lad os ikke skændes. – Let’s not argue.

You can add who you argue with:

De skændes med hinanden. – They argue with each other.
Han skændes med sin bror. – He argues with his brother.

Why is it tale roligt and not tale rolige or tale rolig?

Here roligt is an adverb, modifying the verb tale (“talk”). In Danish, many adverbs are formed from adjectives by adding -t:

rolig (adjective: calm) → roligt (adverb: calmly)
hurtig (quick) → hurtigt (quickly)
klar (clear) → klart (clearly)

So:

en rolig person – a calm person (adjective)
tale roligt – talk calmly (adverb)

rolige would be an adjective form used with plural or definite nouns, e.g.:

de rolige børn – the calm children

Why is the preposition om used in tale roligt om problemet?

In Danish, the common way to say “talk about X” is tale om X (or snakke om X):

tale om noget – talk about something
snakke om vejret – chat about the weather

So:

tale roligt om problemet – talk calmly about the problem

You do not use af here; af usually corresponds to of/from/by in other constructions, but “talk about” is fixed as tale om.

Why is it problemet and not just problem?

Danish uses a definite ending instead of a separate “the” in most cases.

et problem – a problem
problemet – the problem

In this sentence, English would say “the problem”, so Danish uses the definite form problemet:

tale roligt om problemet – talk calmly about the problem

If you wanted to say “talk calmly about a problem”, you could say:

tale roligt om et problem

Could we move i stedet for at skændes to the end of the sentence?

Yes. You can say:

Lad os tale roligt om problemet i stedet for at skændes.

This is also very natural and probably slightly more common in everyday speech. The meaning is the same; you just attach the “instead of arguing” part at the end.

So you have (at least) two good options:

Lad os i stedet for at skændes tale roligt om problemet.
Lad os tale roligt om problemet i stedet for at skændes.

Both are correct; the difference is mainly rhythm and what you put early for emphasis.

Where can i stedet go in the sentence, and is it different from i stedet for at skændes?

In your sentence, i stedet for at skændes is one unit (“instead of arguing”). You can only move it around as a whole:

Lad os i stedet for at skændes tale roligt om problemet.
Lad os tale roligt om problemet i stedet for at skændes.

Just i stedet on its own means simply “instead” and usually refers to the whole action:

Lad os i stedet tale roligt om problemet. – Let’s instead talk calmly about the problem.

Here i stedet is a short adverbial (“instead”). If you want the full comparison “instead of arguing”, you say i stedet for at skændes.

Is the comma before at skændes or tale required in Danish?

In your version there is no comma, and that is perfectly fine under modern Danish comma rules (the “new comma”), which many people use.

Older or more traditional rules (the “grammatical comma”) would sometimes put commas before certain infinitive clauses with at, but even then, not all such cases require a comma.

With current usage, you can safely write:

Lad os i stedet for at skændes tale roligt om problemet.
Lad os tale roligt om problemet i stedet for at skændes.

with no commas, and this will be considered correct and natural.