Air carrier Captain reported becoming unstabilized due to turning onto a short final during a clearance for a visual approach. The Captain directed a go around but the First Officer maneuvered to correct the approach path; received a sink warning; then stabilized the approach.

Narrative

We were on a visual approach to 14 in RAP. FO decided to hand fly. He turned off the automation and turned a tight base leg. As we joined the final approach course; I quickly realized we were very high. He attempted to do a slight S-turn. I told him it was not going to work and to prepare to go around. A few seconds later I told him we are way too high; let's go around". The FO wanted to do a 360 degree turn instead to lose altitude. I called Tower requesting a 360. There was not a response. I radioed Tower again; he did not respond. I looked down at the audio panel and the frequency on the plate thinking I may have accidentally switched it when I put Ground in standby. When I looked up; the FO had put us in a quick right turn. I told him "you cannot do this without clearance." And instructed him to re-join the final. He told me he was cleared for the visual and did not need a clearance. As he brought the wing level to turn back; I again requested clearance to do the maneuver from the controller as we were now off of the final course. I then called for a go around again. Simultaneously; we received the clearance to perform a 360 degree turn. The FO immediately continued the right turn. We rejoined the final at traffic pattern altitude. While back on final; a little under 1000 feet AGL; the FO received a "sink rate" warning as he was correcting from getting high on the approach due to a high thrust setting from the 360 degree turn. I called out the excessive sink rate. The FO added additional power and raised the nose and stabilized on the PAPIs. In hindsight; without a doubt; I should have commanded a go around and stuck with my decision. I realize now that I had initially "casually instructed" the go around as part of a sentence. However; I think the FO did not register the call as I included it within a sentence and he was overwhelmed with the airplane. When we de-briefed; the FO did not recall being told to go around either time. My instruction should have been standalone and clear. Once the decision was made; I should not have reconsidered. Additionally; I should have taken control of the aircraft when he became unresponsive to the go around instruction. I am kicking myself over and over about even entertaining the 360 degree turn. I've never permitted something like this before. This was thoroughly debriefed. Additionally; we thoroughly debriefed what are acceptable maneuvers when cleared for a visual approach in controlled airspace. After our de-brief; the FO understood why he needed an ATC clearance to perform a 360 degree turn maneuver. Additionally; we de-briefed a visual approach set up from the downwind. We discussed the SOP/recommended technique for configuration timing and spacing on visual approaches. When I got to the hotel; I wrote a report and de-briefed the event with a review team. After our de-brief; the FO and I sat down the next day and we de-briefed some additional points."