Først når børnene sover, slapper jeg af.

Først når means only when or not until.

So:

• Når børnene sover, slapper jeg af = When the children are asleep, I relax
• Først når børnene sover, slapper jeg af = Only when the children are asleep do I relax

The word først adds a limiting idea: relaxing happens only after that condition is met.

In this sentence, først når is a very common combination in Danish.

This is because Danish follows the V2 rule in main clauses: the finite verb must come in the second position.

The sentence begins with the subordinate clause:

• Først når børnene sover

After that comes the main clause. Since something other than the subject is in first position overall, the finite verb of the main clause comes before the subject:

• slapper = verb
• jeg = subject

So:

• Først når børnene sover, slapper jeg af.

This is the same pattern you see in sentences like:

• I dag arbejder jeg hjemme.
• Når jeg kommer hjem, laver jeg mad.

If the main clause stood alone, it would be:

• Jeg slapper af.

Because Først når børnene sover is a subordinate clause, and in standard Danish writing it is separated from the main clause by a comma.

So the structure is:

• Subordinate clause: Først når børnene sover
• Main clause: slapper jeg af

Danish comma rules can be a bit different from English, but in a sentence like this, the comma is normal and expected.

Slappe af is a fixed verb expression meaning to relax.

The basic verb is:

• at slappe af = to relax

In a finite clause, Danish often splits this kind of verb expression:

• Jeg slapper af.
• Han slapper aldrig af.

So in your sentence:

• slapper = present tense verb
• af = particle belonging to the verb phrase

You should learn slappe af as one unit, not just slappe by itself.

Because the plural of barn is irregular.

The forms are:

• et barn = a child
• barnet = the child
• børn = children
• børnene = the children

So børnene is the definite plural form: the children.

This is just something you have to memorize, since it does not follow the regular plural pattern.

Sover is simply the normal verb to sleep in the present tense:

• at sove = to sleep
• sover = sleep / are sleeping

In Danish, børnene sover can naturally mean the children are sleeping or, depending on context, the children are asleep.

English often distinguishes between sleeping and asleep, but Danish commonly uses sove in places where English might prefer either one.

Yes, that is also a natural Danish sentence.

Compare the two:

• Først når børnene sover, slapper jeg af.
• Jeg slapper først af, når børnene sover.

Both mean roughly the same thing, but the first version gives stronger emphasis to the condition:

• Først når børnene sover... puts focus right away on only when the children are asleep

The second version is often a bit more neutral in flow, while the first can sound slightly more emphatic or stylistically marked.

It can describe a general habit or a repeated situation.

Danish often uses the present tense for things that happen regularly:

• Først når børnene sover, slapper jeg af.

This can mean something like:

• I only relax once the children are asleep
• I don’t relax until the children are asleep

So it does not have to mean only right now. It can describe a usual pattern in everyday life.

Because Danish does not need that extra helping verb here.

In English, formal or emphatic structures sometimes use do:

• Only when the children are asleep do I relax.

Danish expresses the same idea through:

• først når
• normal Danish word order with the verb in second position

So Danish says:

• Først når børnene sover, slapper jeg af.

There is no separate equivalent of that English do in this sentence.

The sentence already sounds natural, but in everyday speech people might also say things like:

• Jeg kan først slappe af, når børnene sover.
• Jeg slapper først af, når børnene sover.

Adding kan makes it sound like:

• I can only relax when the children are asleep

That can feel especially natural if the speaker means they are too busy or tense before then.

But your original sentence is completely correct and idiomatic.