"Her children are reading."
Translation:Hendes børn læser.
sin/sit/sine is only used to refer back to the subject of a sentence.
Hun tog sit glas.
Hun læser med sine børn.
Apparently "sin"/"sit"/"sine" are what's known as "reflexive possessive pronouns," and are used to refer back to the original subject of the phrase. As such, there must be a subject (which there isn't in this sentence).
Consider the sentence "Jane reads her book." If it's Jane's own book that she's reading, you could use the reflexive possessive pronoun: "Jane læser sin bog;" if it's another woman's book that Jane's reading, you would use the non-reflexive version: "Jane læser hendes bog." As I suggested above, the non-reflexive form would also be used when the subject isn't specified, e.g. "Det er hendes bog."
Here's a great explanation that I found: http://forum.wordreference.com/threads/danish-differences.676806/
Why hendes instead of hende? With sin/sit/sine and din/dit/dine the e at the end implies plural. Is hendes plural for her?
Hendes is possessive and used when she owns something. Hendes mor=her mother, hendes hund=her dog, Hende is used when you refer to her as a person - Jeg kan lide hende=I like her. Jeg kender hende=I know her. BUT Jeg kender hendeS søn=I know her son