  Nuclear spins show exceptionally long coherence times but the underlying good
isolation from their environment is a challenge when it comes to controlling
nuclear spin qubits. A particular difficulty, not only for nuclear spin qubits,
is the realization of two-qubit gates between distant qubits. Recently, strong
coupling between an electron spin and microwave resonator photons as well as a
microwave resonator mediated coupling between two electron spins both in the
resonant and the dispersive regime have been reported and, thus, a microwave
resonator mediated electron spin two qubit gate seems to be in reach. Inspired
by these findings, we theoretically investigate the interaction of a microwave
resonator with a hybrid quantum dot-donor (QDD) system consisting of a gate
defined Si QD and a laterally displaced $^{31}$P phosphorous donor atom
implanted in the Si host material. We find that driving the QDD system allows
to compensate the frequency mismatch between the donor nuclear spin splitting
in the MHz regime and typical superconducting resonator frequencies in the GHz
regime, and also enables an effective nuclear spin-photon coupling. While we
expect this coupling to be weak, we predict that coupling the nuclear spins of
two distant QDD systems dispersively to the microwave resonator allows the
implementation of a resonator mediated nuclear spin two-qubit
$\sqrt{i\mathrm{SWAP}}$ gate with a gate fidelity approaching $90\%$.
