This would mean something like a children's home. It should be: "Their children live at home".
Both your translation and the above one sound fine to me, but yes, yours is a little more natural sounding.
Nice that "their kids live at home" was marked correctly even though it's quite different from the "correct" translation :)
Why don't they accept "Her sons..."?? They are even giving a hint themselves that unke can have a meaning his/her/their but still marking my answer as a wrong one! Stupid!