Your relative's DP earns around £75,000, and she commits fraud that would roughly bring in around another £20,000 of taxable salary, so household income would be edging that of someone on £100,000? And she not only feels no shame about the fraud, or fear of being caught, she actually constantly boasts about it to people, going into minute detail about all her family finances?
And you are on more than double their income, so your household income would be around the £200,000 pa, pre-tax, level?
And for the benefits agency not to be suspicious, she must live in a relatively modest property - I mean, they only pay a capped amount towards a rental, and they presumably insist on seeing a rental agreement. It would be flagged up as possibly/probably fraudulent if that rental was massively higher than the contributory ceiling, no? And people on here say the HB ceiling now is the cheapest 30% of properties, which includes social housing, so probably knocks it down to the cheapest 20% at most, instead. Why are this high earning family living in a dirt cheap rental property instead of buying? Sure, it's free money, but what for, if they have to live somewhere cheap and rented? 
Why is she shopping at what, from a quick recce, looks like the online equivalent of Primark?
I mean, I'm all in favour of non-materialistic, frugal people. But you've described her as extravagant and spendthrift. If they don't have a mortgage and they live somewhere cheap, and her idea of a spendalooza is that site... where the hell is all the cash going?