  We present measurements on gate-defined double quantum dots in Ge-Si
core-shell nanowires, which we tune to a regime with visible shell filling in
both dots. We observe a Pauli spin blockade and can assign the measured leakage
current at low magnetic fields to spin-flip cotunneling, for which we measure a
strong anisotropy related to an anisotropic g-factor. At higher magnetic fields
we see signatures for leakage current caused by spin-orbit coupling between
(1,1)-singlet and (2,0)-triplet states. Taking into account these anisotropic
spin-flip mechanisms, we can choose the magnetic field direction with the
longest spin lifetime for improved spin-orbit qubits.
