It's actually not unusual for a 3-rd party auditors to do Internal Audits.
Most small companies don't have enough employees or independent groups/departments to be able to perform an internal audit by just using internal associates and must hire a consultant or some other external party to do it.
There is nothing wrong for an organization to outsource the internal audit process to competent people, such as certified lead auditors who happen to work for a registrar. However, the original post stated when OUR 3rd-party auditor.... There can be NO conflict of interest and the external 3rd party auditor can NOT be an internal auditor. ISO 17021 prohibits that conflict of interest.
Our third party (registrar) auditor wanted someone certified in doing TS 16949 internal audits, and we do not currently have such a person. We questioned the necessary certification and he relented, but I still wanted someone here that had more experience in doing TS 16949 internal auditing than I have, so we hired an outside auditor. He actually works for our registrar, and had audited us is in the past, and has a very good grasp on TS 16949, so he was able to go line by line through our procedures and make sure they complied with what TS is asking.
I strongly believe that you have been victim of a scam. I will assume the two auditors in question are not full time employees of the registrar that certifies you for TS 16949. Despite the fact that they might be subcontract auditors, the insistence that you had to be internally audited by someone with 16949 qualifications, leads me to believe that you have been taken for a ride that, which, despite being common practice, is not well known.
Contract auditors working for registrars establish relationships among them. As many of them are also "consultants", when they work as an auditor, they find problems that, the other one, working as a consultant, can help the organization with, just like in your case. It is like a perpetual scam where unscrupulous auditants (consultants working as auditors) create work for their colleagues. The expectation is, obviously, the other consultant would reciprocate the favor, later on.
The practice you described is prohibited by ISO 17021, even though is very hard to be policed. If I were you, I would denounce this scam to the IAOB/IATF and let them deal with the auditors in question. Lack of ethics is a big problem in this business.