This error occurs when you have associated a child SKU to multiple parent SKUs.
Invalid variation relationship: The child variation is already assigned to a parent SKU. Please delete the old relationship before submitting a new relationship.
If you upload an inventory file to your selling account where variations are created and wish to reassign your child SKUs to different parent SKUs, you must first submit a delete feed to break the variation family that was created during the initial upload. You will need to do this before assigning a new parent SKU to a child SKU.