  We study spin transport in the one- and two-electron regimes of
parallel-coupled double quantum dots (DQDs). The DQDs are formed in InAs
nanowires by a combination of crystal-phase engineering and electrostatic
gating, with an interdot tunnel coupling ($t$) tunable by one order of
magnitude. Large single-particle energy separations (up to 10 meV) and $|g^*|$
factors ($\sim$10) enable detailed studies of the $B$-field-induced transition
from a singlet-to-triplet ground state as a function of $t$. In particular, we
investigate how the magnitude of the spin-orbit-induced singlet-triplet
anticrossing depends on $t$. For cases of strong coupling, we find values of
230 $\mu$eV for the anticrossing using excited-state spectroscopy. Experimental
results are reproduced by calculations based on rate equations and a DQD model
including a single orbital in each dot.
