To answer the question 'What do you think of this wonderful family?' - not a lot - but it certainly highlights, yet again, the glaring flaws in the benefits system.
If I wrote what I thought about the criminals in this case, I'd probably be banned for foul language. But sometimes only foul language will suffice . . .
As far as I can see your question is in 2 parts, firstly the family are disgusting any form of human slavery is disgusting and should not be allowed.
To answer your second question - what checks do you want to be made? If they were not making absurb claims on the benefit system it would not flag up any issues.