I figured it out, I had to change the YData attribute in the axes.
ch = h.Children(1).Children(); %children of the axes
% moving 2 to 1
lineHandlesCat2 = ch(3);
lineHandlesCat2Marker = ch(4);
set(lineHandlesCat2,'YData',[1,1])
set(lineHandlesCat2Marker,'YData',[1])
% Moving 1 to 2
lineHandlesCat1 = ch(1);
lineHandlesCat1Marker = ch(2);
set(lineHandlesCat1,'YData',[2,2])
set(lineHandlesCat1Marker,'YData',[2])