I was under the impression that a Government sells a bond, with a interest rate the Government sets. How would the Rothschild family buy bonds (Government debt) and ask for a higher interest rate than that was set in the first place?
Government goes to market wanting to sell ~6b of bonds at as low an interest rate as they can achieve. So if the market buys at 1% they take it, if the market only offers 7% then they take it (if it is below the rate threshold at which they won't sell)
If the Gov doesn't sell enough then it defaults as most debt buys are in part to pay off old debt, we saw this within the Eurozone where Spain has to buy at a much much higher rate than it would like.
Rothschild can simply refuse to buy below a set rate, and if the Gov needs their money at that rate then they buy. But it is not really demanding a higher rate?