An alternative that I might even prefer, would be to just fix the original curve while adjusting the attached curve. It's not clear that there would ever be a situation where one wants the original curve to move, especially since in most cases there is no intuitively satisfying assumption about how the original curve should move.
An example is to sketch a line, then sketch a second line attaching somewhere in the midsection of the first. If I then grab the handle where the second line is attached and drag it, the original line moves in a sort of arbitrary way. I can see the presence of some algorithm for moving the line, but it's never what I actually want.
I think in almost all cases, the user wants the original line to stay fixed and the connection point to slide along it. That is after all the behavior when one initially attaches the new line to the old. It's true that with great care one can avoid moving the original curve, but having spent considerable time and effort perfecting the original curve, I really don't want it to change. Sometimes the change is not very perceptible.
So in summary, I feel the default behavior should be that either the original curve is fixed while adjusting the attached curve, or else it would be easy to lock and unlock entire assemblies.