I choose the latter and disagree my interpretation implies a separation. Your saying God can't become flesh by being born from a mortal. I say he's God and can do anything he wants. You've got the problem of Mary's parents having original sin as well. Since we inherited or nature from Adam so did Mary's parents.
Just to clarify, the Orthodox do not accept any doctrine like the RC doctrine of Immaculate Conception. We do not believe that Mary was anything more or less than a fully normal mortal woman. To believe otherwise breaks down the joining of the fully Divine with the fully mortal.
The logical gymnastics are entertaining.
It's a simple formula from freshman logic courses "If A implies B and B equals C than A implies C"
If Mary is the Mother of Jesus and Jesus = God. Than Mary is the Mother of God.
The logic can be broken in one of two ways. Either Mary is not the Mother of Jesus. Or Jesus is not God. Arguments that seem to differentiate between Mother of Jesus and Mother of God imply that the speaker does not believe that Jesus is God (fitting my response to your first argument). Arguments like your second that speak of "natures" attempt to say that Mary was not, in fact, the mother of Jesus. That Jesus was 50% God and 50% Man when we know that it is not so. Such argument are based on human reasoning and opperate in reverse: "We know that Mary can't be very important because those darn Catholics like her so much, so she can't be mother of God"