Hi lil, I loved your post.
you have Nestorianism, from Nestorius, Arch Bishop of Constantinople (ad428), he separated the 2 natures of Christ, so as to make his unity nearly impossible. he was kicked out, but spent the rest of his life in mission work.
On the other side of the coin you have, 'Eutychianism' Eutyches, was an outspoken opponent of Nestorius. he went so far as to say that while there where 2 natures before the incarnation, there was only one composite nature after it, this is also wrong as it implies a third person. Eutyches was condemned ad 448, However was rather dubiously reinstated ad 449 at Ephesus.
Both these where wrong, so basically the dudes in charge of the churches got together to articulate what was the nature of God incarnate.
They had a council meeting at chalcedon in ad 451, although not agreed upon by everyone at the meeting, it has become the basis of what we believe today.. they called this as Jordan says Hyostatic union (hypostasis).
basically put: the incarnation involved: the union in one person of a full human nature and a full divine nature. Chalcedon expressed this in careful balance: the two natures are united in this hypostatic (i.e, personal) union 'without confusion , without change, without division, without separation'.
You made total sense to me lil
this we do have in common with RC's,.
How Jesus got Hios sinless nature, is a different story and where I believe the RC's Have went unbiblical.
Hope that helps a little bit lil. it probably won't as my spelling and grammer are not the best..
phil