No, it only means within their family structure he has greater authority. That does not lessen her human nature at all. So then, the argument that Jesus submitting to the Father does not make your case that he does not share the very nature of God.
Authority has nothing to do with nature.
Trinitarians throughout the ages teach the Father is greater in authority but not nature. The bible is clear on that. But that teaching is not found in the Bible either. No, it only means within their family structure he has greater authority. That does not lessen her human nature at all.