  Neutral alkaline earth(-like) atoms have recently been employed in atomic
arrays with individual readout, control, and high-fidelity Rydberg-mediated
entanglement. This emerging platform offers a wide range of new quantum science
applications that leverage the unique properties of such atoms: ultra-narrow
optical "clock" transitions and isolated nuclear spins. Specifically, these
properties offer an optical qubit ("o") as well as ground ("g") and metastable
("m") nuclear spin qubits, all within a single atom. We consider experimentally
realistic control of this "omg" architecture and its coupling to Rydberg states
for entanglement generation, focusing specifically on ytterbium-171
($^{171}\text{Yb}$) with nuclear spin $I = 1/2$. We analyze the $S$-series
Rydberg states of $^{171}\text{Yb}$, described by the three spin-$1/2$
constituents (two electrons and the nucleus). We confirm that the $F = 3/2$
manifold -- a unique spin configuration -- is well suited for entangling
nuclear spin qubits. Further, we analyze the $F = 1/2$ series -- described by
two overlapping spin configurations -- using a multichannel quantum defect
theory. We study the multilevel dynamics of the nuclear spin states when
driving the clock or Rydberg transition with Rabi frequency $\Omega_\text{c} =
2 \pi \times 200$ kHz or $\Omega_\text{R} = 2 \pi \times 6$ MHz, respectively,
finding that a modest magnetic field ($\approx200\,\text{G}$) and feasible
laser polarization intensity purity ($\lesssim0.99$) are sufficient for gate
fidelities exceeding 0.99.
