Translation:His parents are selling vacation homes.
"push" is most odd. I think the only thing that can be "pushed" in this way are illegal drugs, not holiday homes
To me "push" signifies that the seller is trying to convince the buyer to buy something. A good example would a salesperson "pushing" extended warranties along with the standard product.
@yaqo: It means that someone is selling drugs illegally. (in this context 'to push' = to sell)
And why is "His parents sell cottages" wrong?
To me a cottage is just a small house, so I wouldn't translate it like that. However, I know in some parts of the world it is used to mean a holiday home (I might say holiday cottage to mean that). Otherwise it seems fine to me. My guess is that the software simply doesn't have cottages listed as a translation of Ferienhäuser.
Sein can mean Your (formal) or his, so why do these translations typically use his only?