Open Question: Insurance billing, primary vs secondary-- any advice is helpful?

Scenario: Primary insurance is Medicare. My secondary insurance is being billed by a company who is not a Medicare provider. The secondary insurance will not pay until Medicare has been billed. The company is requesting my Medicare card and being very slow and vague about what exactly they are doing. Does anyone know the procedure for this? I feel like both companies are trying to blame me somehow and am worried no one will end up paying