You're right. The pod is debalancing your vessel.
I'm no expert in this, but you should perhaps consider "attachment" mechanism instead of docking... Either that, or make a
docking port which is on the longitudinal axis of your craft.. Directly in the front or directly on the back of the vessel's
vector of movement. All other points will rotate the vessel..
With DG3 astronauts it's a different system. The astronauts are created by code, when you go EVA and deleted after you
re-enter DG3. They don't dock to the vessel and they don't directly affect the mass - the code probably adds and substracts
their weight depending on whether they are in our outside of the vessel...