This paper introduces a hybrid dynamical system methodology for managing impulsive control in spacecraft rendezvous and proximity operations under the Hill-Clohessy-Wiltshire model. We address the control design problem by isolating the out-of-plane from the in-plane dynamics and present a feedback control law for each of them. This law is based on a Lyapunov function tailored to each of the dynamics, capable of addressing thruster saturation and also a minimum impulse bit. These Lyapunov functions were found by reformulating the system's dynamics into coordinates that more intuitively represent their physical behavior. The effectiveness of our control laws is then shown through numerical simulation.