Due to the challenges regarding the limits of their endurance and autonomous capabilities, underwater docking for autonomous underwater vehicles (AUVs) has become a topic of interest for many academic and commercial applications. Herein, we take on the problem of relative navigation for the generalized version of the docking operation, which we address as proximity operations. Proximity operations typically involve only two actors, a chaser and a target. We leverage the similarities to proximity operations (prox-ops) from spacecraft robotic missions to frame the diverse docking scenarios with a set of phases the chaser undergoes on the way to its target. We emphasize the versatility on the use of factor graphs as a generalized representation to model the underlying simultaneous trajectory estimation and relative navigation (STERN) problem that arises with any prox-ops scenario, regardless of the sensor suite or the agents' dynamic constraints. To emphasize the flexibility of factor graphs as the modeling foundation for arbitrary underwater prox-ops, we compile a list of state-of-the-art research in the field and represent the different scenario using the same factor graph representation. We detail the procedure required to model, design, and implement factor graph-based estimators by addressing a long-distance acoustic homing scenario of an AUV to a moving mothership using datasets from simulated and real-world deployments; an analysis of these results is provided to shed light on the flexibility and limitations of the dynamic assumptions of the moving target. A description of our front- and back-end is also presented together with a timing breakdown of all processes to show its potential deployment on a real-time system.