BE-20 pilot reported the aircraft began rolling forward while parked with engines running. The co-pilot applied brakes to stop the roll and then attempted to turn the aircraft in a tight area. The nosewheel became jammed and the co-pilot applied strong rudder inputs to free it so the aircraft could taxi.

Narrative

I was the company's designated PIC on a Part 135 flight from ZZZ-ZZZ1. Our company's Chief Pilot preceded me onboard the aircraft; and while I was securing the (aft) entry door; I heard the engines starting. Although I did not authorize the Chief Pilot to start the engines; I finished securing the door; ensured the (2) passengers were seated with seats belts and harnesses fastened; and continued to the flight deck. While I was moving into my seat and securing my harness; I asked the Chief Pilot if he had the aircraft; and he responded that he did. Upon sliding my seat forward; I looked out of the windscreen and noticed the aircraft was rolling forward. Once again; I asked the Chief Pilot if he had the aircraft; and he said he did and the parking brake was on. I responded the parking brake was on but the aircraft was still rolling. At that point the Chief Pilot slammed on the brakes. Because we rolled forward; the marshaller signaled for us to shutdown so that he could push us back so that we would avoid hitting a car parked in front of us. However; the Chief Pilot felt we could make the turn without shutting down/pushing back and asked me my opinion. I was unsure whether we could make the turn or not but told him that we would have to use high power on the outboard engine and beta on the inboard and that 'politically' the optics would be ugly. Nonetheless; the Chief Pilot insisted we attempt the turn and signalled the marshaller accordingly. We successfully avoided the parked car on our right; but the nosewheel became jammed in against the left stop. On our left was a small jet; and when I could not straighten the nosewheel; the Chief Pilot took control of the aircraft. After harshly manhandling the rudder pedals; the Chief Pilot was able to move the nosewheel into a right turn away from the jet. As he taxiied forward; he said initially the nose wheel steering felt funny but then felt normal. He then handed the aircraft back to me; and we departed and landed normally.In retrospect; when the Chief Pilot asked if I thought we could make the turn; I should have acted as PIC and shutdown the engines.