Både min fætter og min nevø spiller kort med os, mens min niece tegner ved bordet.

Både ... og means both ... and.

So:

• Både min fætter og min nevø = both my cousin and my nephew

It is a fixed pairing in Danish:

• både X og Y = both X and Y

This is very common and works much like English.

In Danish, the present tense verb does not change according to person or number.

So:

• jeg spiller = I play
• du spiller = you play
• han spiller = he plays
• vi spiller = we play
• de spiller = they play

Because of that, spiller is used whether the subject is one person or several people. English changes play / plays, but Danish does not.

In Danish, spille kort is a standard expression meaning to play cards.

Here, kort is used in a general sense, just like English play cards. It does not usually need an article.

Compare:

• spille kort = play cards
• spille fodbold = play football / soccer
• spille skak = play chess

So kort here is part of the expression, not referring to specific cards.

After a preposition such as med, Danish uses the object form of the pronoun.

So:

• vi = we
• os = us

That means:

• med os = with us

This is the same idea as in English:

• not with we
• but with us

Other examples:

• til ham = to him
• for hende = for her
• uden dem = without them

Mens means while.

It introduces a subordinate clause:

• mens min niece tegner ved bordet = while my niece is drawing at the table

In Danish subordinate clauses, the word order is different from main clauses when an adverb is involved. In this sentence, there is no adverb like ikke or altid, so the clause looks straightforward:

• min niece tegner ved bordet

But compare:

• Main clause: Min niece tegner ikke ved bordet
• Subordinate clause: ... mens min niece ikke tegner ved bordet

So mens is both a meaning word (while) and a grammar signal for a subordinate clause.

Because fætter, nevø, and niece are all common gender nouns in Danish, so they take min in the singular.

Danish has two grammatical genders:

• common gender → en, min
• neuter → et, mit

So:

• min fætter
• min nevø
• min niece

If the noun were neuter, you would use mit instead.

In Danish, when you use a possessive such as min, you do not also use an indefinite article.

So:

• min fætter = my cousin
• not en min fætter

This is the same basic idea as in English: you say my cousin, not a my cousin.

The possessive already determines the noun.

These are family terms:

• fætter = male cousin
• nevø = nephew
• niece = niece

A useful extra word is:

• kusine = female cousin

So Danish often distinguishes male and female cousin with different words:

• fætter = male cousin
• kusine = female cousin

English usually just says cousin unless the gender matters.

Ved bordet means at the table or by the table.

• ved often means by, near, at
• på bordet means on the table

So:

• tegner ved bordet = drawing at the table
• tegner på bordet = drawing on the table

That second one would mean the person is drawing directly on the surface of the table, which is probably not the intended meaning.

Bordet is the definite form, meaning the table.

Danish often attaches the definite article to the end of the noun:

• et bord = a table
• bordet = the table

So ved bordet literally means by the table / at the table.

This is one of the most important patterns in Danish grammar.

Yes. Danish word order is flexible, but if you move an element to the front of a main clause, the finite verb normally comes second.

For example, you can say:

• Både min fætter og min nevø spiller kort med os, mens min niece tegner ved bordet.

You can also begin with the subordinate clause:

• Mens min niece tegner ved bordet, spiller både min fætter og min nevø kort med os.

Notice that in the second version, after the fronted mens-clause, the main clause begins with the verb spiller before the full subject phrase. That is normal Danish verb-second word order.

Yes, it is very natural.

The basic structure is:

• subject: Både min fætter og min nevø
• verb: spiller
• object/expression: kort
• prepositional phrase: med os

So the sentence flows naturally as:

• Både min fætter og min nevø spiller kort med os

Danish word order can sometimes be adjusted for emphasis, but this version is neutral and idiomatic.

A learner will often notice the letters æ and ø.

• æ in fætter is somewhat like the vowel in English cat, though not exactly the same.
• ø in nevø is a rounded front vowel that English does not really have. Many learners approximate it at first.

A rough learner-friendly guide:

• fætter ≈ FEH-ter
• nevø ≈ neh-VUH / neh-VOE with rounded lips on the last vowel
• niece ≈ nee-se

These are only approximations. Danish pronunciation is often less direct than spelling suggests, so it helps to hear native audio.

Because in modern Danish, common nouns are not capitalized.

So you write:

• min fætter
• min niece
• bordet

This is different from German, where all nouns are capitalized, but similar to English. Only proper names and sentence beginnings are capitalized.