I would say... 1. The children destroyed the playing facilities on the playground. 2. The housewives left the family trash in the street. ("on the street" is also acceptable, but....)

I'll add that "family trash" and "playing facilities" don't sound natural in English. You would probably hear them phrased like this: 1. The children destroyed the facilities on the playground. (Or just "destroyed the playground" or "the structures on the playground") 2. The housewives left the trash in the street. OR The housewives left the family's trash in the street. OR The housewives left their trash/their family's trash in the street. (If there isn't any other context given beforehand)