Hi. I know this will sound discouraging but went thru that process of getting an appropriate government accommodation several months back and it took me more than a month before I gave up. Luckily they opened a new housing complex for my company so after 5 weeks of going back and forth to the government housing office, I stopped going and I am living now in my company provided housing which I got directly from my company.

Given your situation, it would be best if you can delay your family's arrival or get an appropriate accommodation for them for the time being.