A Tower Controller reported an aircraft turn final in front of the aircraft it was supposed to follow resulting in the trailing aircraft reporting a NMAC. The reporter stated they warned the Local Controller and their Trainee of the impending confliction but neither one of them took timely action to resolve the situation.

Narrative

Controller Y was training on local 1 with Controller Z as trainer. I noticed Controller Y cleared Aircraft X number 2 when he should have been number three and said 'number three?' There was no response and I looked at the trainer who didn't seem to care. I looked back a bit later and noticed Aircraft X had turned in front of the aircraft he was supposed to follow and pointed it out as did the ground controller. Controller Y did not take any action so I told him to send the cub around. He eventually figured out the call sign and told him to go around. I noticed Aircraft X was still continuing towards the runway and Aircraft Y was right behind and gaining fast. I shouted that Aircraft X was still pointed at the runway and told Controller Y to turn him now. He paused for a long while and then issued traffic to the Cub for a helicopter instead. I noticed the Aircraft X had started to go around and had assumed he just was slow to follow the instruction. I later found out that not only had Aircraft X never acknowledged the go around instruction; but that the pilot of Aircraft X actually keyed up 3 times and told him to go around before he finally did. At this point; Aircraft X was over the numbers and the Dakota was approximately 400 feet behind and closing. The trainer never attempted to let up and the CIC (controller in charge); Controller A who is a sup; never filed a report even though the pilot reported an NMAC.Controller Y has consistently been a danger especially in the last couple months of his training. Multiple trainers have expressed that they don't want to train with him and he is 'scary and dangerous.' Even after the ATM was made aware of the multitude of separation busts consistently made on a daily basis and having witnessed one bad one himself; had failed to stop his training. Controller A also did not recommend a suspension after witnessing many himself. They insisted he needed to 'just finish his hours;' despite every single controller telling every member of management how dangerous he was. There were also many many complaints voiced of Controller Z as a trainer who does not pay attention; does not keep a traffic pad; and does not step in when necessary. Management has failed at every single turn to ensure that safety was maintained despite the complaints and reports of every single controller in the facility. This is not an exaggeration. I'm only surprised it took this long to happen. Had the pilot of Aircraft Y not been an experienced pilot; known the pilot and call sign of the aircraft that was ahead; and is also a controller; I think there would have been an accident. Due to traffic; he was not able to make any evasive maneuver other than to fly between the two runways and hope no one turned into him. The trainee's training needs to be terminated immediately as a concern for safety. Controller Z needs to be de-certified as a trainer immediately. Management needs to be held accountable as to why this incredibly unsafe situation was allowed to continue for months; even though they had dozens of complaints about both Controller Y and Controller Z as well as another trainer who was of a similar dangerous training caliber. Management was warned over and over that something like this would happen; and they did absolutely nothing and I hold them directly responsible for this. They also failed to make any report whatsoever. This is not the first time but one of many that such incidents have been 'swept under the rug' and this needs to be investigated. This was completely avoidable and nearly tragic.