Many quantum gate proposals make physical assumptions to ease analysis. Here we explicitly consider the effect of these assumptions for a particular two-qubit gate proposal, a cube-root-of-unity gate, in which the two qubits are donors in a semiconductor coupled via an intermediate 'control' spin. Our approach considers directly the electronic structures of the qubit and control impurity systems. We find that such gates are highly sensitive to environmental factors overlooked in analytically soluble models, but that there are regimes in which simplifying assumptions are valid and lead to high fidelity gates.