You'd probably get better results by animating the branches using bones. By using bones you also get the benefit of being able to animate using rotation properly.
What do I mean by that?
If you take a look at the following image.
Loading Image
The blue square is rotated 45 degrees. If the mesh points are selected, rotated and then keyed, the path they will take is the shortest distance (the purple lines).
If you rotate the bone the mesh is attached to the vertices will follow the red line.
Here's a vine of an old project I did. The branch could just be copied and placed elsewhere and keys offset to make it look like the branches are growing along with the main stem.
https://vine.co/v/M9u5pxvLYqK