  Quantum dot hybrid qubits exploit an extended charge-noise sweet spot that
suppresses dephasing and has enabled the experimental achievement of
high-fidelity single-qubit gates. However, current proposals for two-qubit
gates require tuning the qubits away from their sweet spots. Here, we propose a
two-hybrid-qubit coupling scheme, based on exchange interactions, that allows
the qubits to remain at their sweet spots at all times. The interaction is
controlled via the inter-qubit tunnel coupling. By simulating such gates in the
presence of realistic quasistatic and $1\!/\!f$ charge noise, we show that our
scheme should enable controlled-$Z$ gates of length $\sim$5~ns, and Z-CNOT
gates of length $\sim$7~ns, both with fidelities $>$99.9\%.
