I am not sure what is different about your curve that is away from and edge, but have you tried fully defining the location of the point before you add the tangencies? That might stop the system from moving the center point.
Why do you wan to put that curve away from the edge? I would start out by placing it on the edge without a curve and see if that gave you a good enough surface.
There are a couple of ways to do this type of bridge curve. My favorite method (and most robust constraint) is to use the tangent face and curvature to face end condition. It is somewhat undiscoverable but here is what you do: Click on the spline, then hold down contrl key, and click on the edge that it is connected to (the boundary of the solid face that you want to make tangent to, then click on the face of the suraface you want to be tangent to. With all three selected you should get tangent face or Curvature face constraint to make.
BTW, If your parent features are going to change a lot, I would only do one 3D sketch curve per sketch. The 2014 Style spline is excellent for this type of bridge curve application.