He does have a duty to obey her, as His mother. As a human being, He was bound to obey His own commandments. In fact, at the Wedding at Cana, He does.
Where it’s not working for you is that you assume that Her will would be any different than His. I’m not trying to convince you of the Immaculate Conception, but if you for argument’s sake, in order to understand our point, assume that Mary was sinless, then you could agree that her will, since she never sinned, never went against His. So there would be no problem with Him obeying her.
That’s a great argument by the way. If He was truly human and God, then, yes, in order not to sin he would have to obey her. He would have to be the perfect human (which He is). The only way He could in good conscience always obey her, since He’s God, would be if her instructions were always correct. So, if Jesus if both fully God and man (which I assume you believe He is), He would only be able to sinlessly obey His mother if she were always in accordance with God’s will.