  We consider Anderson transitions in two-dimensional spinful electron gases
subject to random scalar potentials with time-reversal-symmetric spin-mixing
tunneling (SMT) and spin-preserving tunneling (SPT) at potential saddle points
(PSPs). A symplectic quantum network model, named as SMT-QNM, is constructed in
which SMT and SPT have the same status and contribute independent tunneling
channels rather than sharing a total-probability-fixed one. Two-dimensional
continuous Dirac Hamiltonian is then extracted out from this discrete network
model as the generator of certain unitary transformation. With the help of
high-accuracy numerics based on transfer matrix technique, finite-size analysis
on two-terminal conductance and normalized localization length provides a phase
diagram drawn in the SMT-SPT plane. As a manifestation of symplectic ensembles,
a normal-metal (NM) phase emerges between the quantum spin Hall (QSH) and
normal-insulator (NI) phases when SMT appears. We systematically analyze the
quantum phases on the boundary and in the interior of the phase space.
Particularly, the phase diagram is closely related to that of disordered
three-dimensional weak topological insulators by appropriate parameter mapping.
At last, if time-reversal symmetry in electron trajectories between PSPs is
destroyed, the system falls into unitary class with no more NM phase. A direct
SMT-driven transition from QSH to NI phases exists and can be explained by
spin-flip backscattering between the degenerate doublets at the same sample
edge.

Mesoscale and Nanoscale Physics