Yes you can conduct internal audits as a QA Manager or QA Employee. However, you cannot audit your own programs. This does make it hard because many of the general categories are technically "owned" by QA, but there are items in an audit that can be audited by a member of the QA Team.
The auditor was likely talking about parts of the process where your relative owned the process. For example, I would imagine as a QA Manager, she owned the HACCP program. If she conducted an internal audit on HACCP, then that would be a violation of the standard. This would have to be done by someone outside of QA, or at least by someone who isn't responsible for HACCP at all.
It is my understanding that the auditor's position was that they could not conduct the internal audit. This may be due to just what your saying - the auditor had already determined that there was enough areas or even one that they were not "independent of". that was not communicated though.
The question was can you conduct the internal audit yourself. Its not a yes and no answer. You can not audit areas that you are "independent of" as you stated. One would need to make sure that they could justify that the internal auditor was independent of the function being audited. I could potentially see an aggressive auditor stretching "independent of" pretty far.