Inflation may be occurring domestically in the US but the rest of the world is demanding dollars as well, offsetting the money supply increase by a significant margin. This is when the interest rates will start to rise in an attempt to slow demand, since the unlikely alternative of simply introducing more dollars at a pace sufficient to handle the demand has become politically unpalatable.
I believe what you are saying is by raising interest rates on bonds, then demand for bonds can be reduced because investors will anticipate further interest rates hikes thus devaluing the already issued bonds at lower interest rates. Thus discouraging capital to convert FOREX to buy dollar bonds.
And this selloff of bonds will ignite a frenzy of buying in the stock market.
Yes, that is one aspect at the institutional level although I think bonds will be bid on by large entities in an effort to support the financial system despite the intended psychological effect. That supportive effort will fail, of course.
A larger impact I see is that USD denominated loan rates will rise, eventually building the incentive to acquire funds in other denominations which will outweigh the demand during a wave of defaults. Even as rates rise and return for loans provided increases, there will be less lending bid on and the lion's share of capital will indeed flow into equities.
What borrower wants to pay back on something that has appreciated significantly, and at a higher rate than other sources? That will be exacerbated by newer tools making alternative denominations easier to handle. See
Align Commerce as an example.