Try the simple and easily accessible things first before you start tearing into the boat, such as the breaker and everything on that circuit.
Breakers DO go bad, as mentioned. I would try that.
Before you buy a new breaker, is there an equal value breaker in the panel that you can temporarily swap out? Or is this some kind of main breaker for the shore power?
Forgive me, I'm not familiar with the term auxiliary breaker.
I'm guessing the breaker keeps tripping and cannot be reset. Try removing the load wires from the breaker. Can you reset it after that?
I'm an electrician, but not really familiar with shore power on boats. This is a bit different than wiring a high rise building in Manhattan.
Check the condition of any loads on that circuit. Check those outlets you mentioned that are not working. Open them up and check for corrosion at any of the connections.
Good luck. Keep us posted...