How to design a circuit starting from a block diagram?
It's an exercise in analysis, or algebraic trickery if you will ;-)

Please excuse the handwritten solution. It took several coffees! Your transfer function is correct. The trick is to see that it can correspond to the gain of a differential amp, where the resistors have 4 independent values. (To simplify the working a bit, I use "Vn" for the + and - inputs of the op amp, which are at the same potential of course.)

At the end I do a sanity check by putting some notional voltages of 1V and 2V and seeing that the result makes sense. I think it is OK.