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.