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. If you have a son and you have authority over him, I can not argue that proves he is not human as the WTS does regarding Jesus.
Authority has nothing to do with nature.
Trinitarians throughout the ages teach the Father is greater in authority but not nature. Jesus shares the same nature with the Father. The bible is clear on that. No, it only means within their family structure he has greater authority. That does not lessen her human nature at all.