I have two curves, one branching off of another. But the child branch doesn't start at a vertex of the parent branch. The first vertex of the child does lie exactly along an edge of the parent, however.
I've been wracking my brains trying to figure out how to insert a vertex in the parent branch that exactly coincides with the first vertex of the child branch but so far it eludes me.
In reality my geometry is much more complex than this with multiple child branches coming off of a single parent as well as many generations of branches. But this is the most reductive case.