Learn Danish: Børnene kysser deres mor godnat. - The children kiss their mother good night.

In Danish, the reflexive possessives (sin, sit, sine) are only used when the subject is singular (he, she, or it). Because the subject here is plural (børnene / they), you must use deres for "their", even when they are doing something to their own mother.

Why is godnat written as a single word rather than god nat?

When used as a fixed greeting or a routine action (like kissing someone "goodnight"), it is written as one word in Danish. You would only write it as two separate words (en god nat) if you were describing a night that was literally pleasant, such as "we had a good night."

How does the word barn (child) become børnene (the children) here?

Barn is an irregular noun. Its indefinite plural is just børn (children), without an -er ending. Because the plural word ends in a consonant, you simply add the standard plural definite ending -ene to get børnene.

Does the structure for kissing someone goodnight map directly to English?

Yes, the structure kysse nogen godnat (to kiss someone goodnight) is a set expression that works exactly like English. You do not need any extra prepositions between the person receiving the action (deres mor) and the greeting (godnat).