The motion of a pod after a collision with a space station would continue in a combined manner according to momentum conservation, with the final velocity calculable via the initial reference frame and conservation laws. Inelastic collisions result in kinetic energy loss, which is the same in any reference frame.
After a collision in space, such as between two satellites or other objects, the motion of the pods compared to the space station depends on conservation laws. In a closed system without external forces, both the momentum and center of mass remain constant before and after the collision. If it's an inelastic collision, where the objects stick together, the two will move together at a velocity that conserves the system's momentum. If the collision is elastic, they may bounce off each other, exchanging kinetic energy but still conserving the total system momentum.
For example, if two satellites collide and dock, which is an inelastic collision, their final velocity can be calculated by using the frame of reference in which one satellite was originally at rest. Loss of kinetic energy will occur due to the conversion of motion into other forms of energy (like heat), but this loss will be the same in either reference frame since kinetic energy is relative to the reference frame, but the energy converted to other forms is not.
To explain the method by which an astronaut can move within the International Space Station without exerting a force on any solid object, one would refer to the conservation of momentum. The astronaut could change position by throwing an object in the opposite direction—thus invoking Newton's third law of motion: for every action, there is an equal and opposite reaction.