Existing bondholders can't demand anything of course. But the bond price is determined by buyers and sellers. With dropping USD, buyers will pay a lower price for the bonds, i.e. the yield will go up.
Your model is missing the Fed, which can buy an almost infinite number of bonds to bring the effective interest rate down to whatever it wants.
Your model is missing the Fed, which can buy an almost infinite number of bonds to bring the effective interest rate down to whatever it wants.