  A fundamental design challenge for quantum dot spin qubits is to extend the
strength and range of qubit interactions while suppressing their coupling to
the environment, since both effects have electrical origins. Key tools include
the ability to retune the qubits, to take advantage of physical resources in
different operating regimes, and to access optimal working points, or "sweet
spots," where dephasing is minimized. Here, we explore an important, new
resource for singlet-triplet qubits: a transverse sweet spot (TSS) that enables
(i) direct transitions between qubit states, (ii) a strong, charge-like qubit
coupling, and (iii) leading-order protection from electrical fluctuations. Of
particular interest is the possibility of transitioning between the TSS and
symmetric operating points while remaining continuously protected. This
arrangement is ideal for coupling qubits to a microwave cavity, because it
combines maximal tunability of the coupling strength with leading-order noise
suppression. We perform simulations with $1/f$-type electrical noise,
demonstrating that two-qubit gates mediated by a resonator can achieve
fidelities $>99$\% under realistic conditions. These results greatly expand the
toolbox for singlet-triplet qubits.
