Robotic tree pruning requires highly precise manipulator control in order to accurately align a cutting implement with the desired pruning point at the correct angle. Simultaneously, the robot must avoid applying excessive force to rigid parts of the environment such as trees, support posts, and wires. In this paper, we propose a hybrid control system that uses a learned vision-based controller to initially align the cutter with the desired pruning point, taking in images of the environment and outputting control actions. This controller is trained entirely in simulation, but transfers easily to real trees via a neural network which transforms raw images into a simplified, segmented representation. Once contact is established, the system hands over control to an interaction controller that guides the cutter pivot point to the branch while minimizing interaction forces. With this simple, yet novel, approach we demonstrate an improvement of over 30 percentage points in accuracy over a baseline controller that uses camera depth data.