Global 5000 Captain reported as pilot not flying; PNF; the pilot flying; PF; performed two unstabilized visual approaches; and the Captain called for two separate go-arounds. The Captain indicated the PNF became situationally unaware of the aircraft state and the procedure steps for the go-arounds. The Captain then took over the controls; and performed a safe landing and conducted a debrief after the flight with the FO.

Narrative

2 Go Arounds and a Control Takeover. We were cleared for a visual approach to Runway XX at ZZZZ. I was the PM in the right seat. The PIC Person A was Pilot flying (PF). The first attempt to land they started the pattern at 2400 MSL. I programmed a 5 mile final to the runway with a 3 degree path to the runway. Person A was concerned that they could not see the runway from a right downwind in the left seat as well as the rising terrain on the final approach to Runway XX. On this attempt to land they were fixated on not getting an Enhanced Ground Proximity Warning System (EGPWS) warning and ended up high on final and fast. I called for a go around. The go around maneuver was executed; albeit sloppy procedurally. We leveled off at 2200 and executed a visual right pattern for a second attempt. I found myself very alert to the control manipulation; pattern; and ability to fly the visual approach. While I coached them to fly slower and which visual reference to use when turning from downwind to base; as I could see the runway; I failed to reload the center line and path to the runway. I was forced to extend all of my attention to their flying. They continued to fixate on the terrain and appeared more concerned with not getting a GPWS alert than flying a constant descent profile; on a target speed. They turned final and were fast. At approximately 500 ft. AGL they were slowing yet still above a stable approach. I was watching the trend and opted to let them continue in hopes they would recover to a safe speed. They did not. At approximately 300 ft. AGL I called for a go around. They did not execute the maneuver. I called again for a go around; and again they did not execute the maneuver. Finally at approximately 100 ft. AGL on my third call for a go around did they execute the procedure. On the climb they appeared unaware of the state of the aircraft; nor proper go around protocol. They were at full throttle climbing and about to over speed. I told them to check their speed and they slammed the throttles to idle in a nose high attitude on upwind. This is when I called 'My Controls'. They did not yield the controls; and again I called for 'My Controls' and this time they relinquished them to me. I continued to fly the third visual pattern and approach to Runway XX; performing a normal; uneventful landing. After landing; the passengers questioned me about what happened. I told them that normally we land on Runway YY; however this time the winds were favoring Runway XX. I explained there was terrain in the area and that our first approach was too high. I continued to say that the second approach was too fast and therefore I made the landing from the right seat.After the passengers departed; I went to the back of the plane to decompress and sort out what had happened; and what to do next. After 15 minutes or so; I asked Person A to speak with me in the cockpit. They started to make excuses for what happened. A right hand pattern from the left seat is obviously more challenging and adding in rising terrain on a final. However I reminded them that they did not listen to my instructions and did not even notice that I had programmed in a center line and vertical path to the runway. They continued to fixate on the potential of a GPWS alert; seemingly unaware of other factors. I acknowledged that I failed to reset the center line for the second attempt; yet my attention was focused on them safely executing a visual approach and landing. I also admit that I should have called for the go around at 500 ft. AGL rather than giving any latitude for them to correct. In my judgment the trend was towards slowing; yet it did not happen as needed; therefore I called for the go around at 300.Suggestions are that age is a primary factor. The PIC turns xx this year. While they are still sharp in some respects; there are areas where they are falling short. In my observation the fixation in this case on GPWS contributed to their inability to fly a standard; stable approach to landing. In addition; they mentioned that they rarely hand-fly a pattern. They did not appear comfortable using the autopilot to maneuver the plane and had disconnected the autopilot. On the initial approach they failed to notice that a center line and vertical path had been programmed. They appeared to be task saturated just flying the plane and fixating. The go around procedure on the first attempt to land was weak. This became even more apparent on the second attempt. They told me that on both go arounds that they did not use the TOGA button. They told me that they felt it was too aggressive; therefore they manually flew it. I do not recall this as I was busy with my PM duties. I feel that our training has allowed less than good performance of maneuvers to pass. We practiced the go around in last year's simulator cycle; and I observed another older pilot who performed poorly doing the same thing. I do not know how Person A worked in their training but their execution of the maneuver was slow; and not to standardize.