  A new quartic force field for the SO$_2$ $\tilde{\text{C}}$$^1$B$_2$ state
has been derived, based on high resolution data from S$^{16}$O$_2$ and
S$^{18}$O$_2$. Included are eight $b_2$ symmetry vibrational levels of
S$^{16}$O$_2$ reported in the first paper of this series [G. B. Park,
$\textit{et al.}$, J. Chem. Phys. $\textbf{144}$, 144311 (2016)]. Many of the
experimental observables not included in the fit, such as the Franck-Condon
intensities and the Coriolis-perturbed effective $C$ rotational constants of
highly anharmonic $\tilde{\text{C}}$ state vibrational levels, are well
reproduced using our force field. Because the two stretching modes of the
$\tilde{\text{C}}$ state are strongly coupled via Fermi-133 interaction, the
vibrational structure of the $\tilde{\text{C}}$ state is analyzed in a
Fermi-system basis set, constructed explicitly in this work via
$\textit{partial}$ $\textit{diagonalization}$ of the vibrational Hamiltonian.
The physical significance of the Fermi-system basis is discussed in terms of
semiclassical dynamics, based on study of Fermi-resonance systems by Kellman
and coworkers [M. E. Kellman and L. Xiao, J. Chem. Phys. $\textbf{93}$, 5821
(1990)]. By diagonalizing the vibrational Hamiltonian in the Fermi-system
basis, the vibrational characters of all vibrational levels can be determined
unambiguously. It is shown that the bending mode cannot be treated separately
from the coupled stretching modes, particularly at vibrational energies of more
than 2000 cm$^{-1}$. Based on our force field, the structure of the Coriolis
interactions in the $\tilde{\text{C}}$ state of SO$_2$ is also discussed. We
identify the origin of the alternating patterns in the effective $C$ rotational
constants of levels in the vibrational progressions of the symmetry-breaking
mode, $\nu_\beta$ (which correlates with the antisymmetric stretching mode in
our assignment scheme).
