This is not necessarily the answer you are looking for, but I'll offer what I can. Please be aware that this is a best guess about the anatomical roots of this sort of issue, based on the current research, personal observations, and the application of data processing analogies (I troubleshoot computer systems for a living). It's really more of a prolonged clarification than an answer, but I hope it helps.
Most of the evidence supporting the anatomical roots for the issues you describe happen to come from research on cadavers of athletes with sports related injuries, because they offer comparative information for the same individual before and after introducing abnormalities into the system. The same symptoms can be a function of metabolic irregularities, mechanical disfunction, or anatomical (developmental or genetic) defects.
If you have not seen a neurologist, I'd suggest doing so, because they can quickly identify or rule out large abnormalities that might be causing issues and recommend courses of treatment.
I specify large abnormalities because the state of the art in brain imaging has only about 3mm resolution (2018). In spite of all the brain scans etcetera, the only reason we know I have an injury is because people around me noticed changes in behavior and cognitive function. At 1mm expected width, my injury is too small to be seen in current generation brain scans, but my history of competition in martial arts for many years and the specific changes noted are consistent with what is known from studies of football player and boxer history and cadavers.
In your son's case, you don't know if the issues are due to birth defect, metabolic issues, injury, or something completely unrelated to anything I know. The current medical tests are simply not sufficiently sensitive to give that kind of detail unless there a a massive anatomical abnormality that can be seen in an MRI or SPECT scan.
Normal processing of emotions is an intensive set of functions involving different specific parts of the brain and multiple communication lines between them. From studies of sport injuries, we know that severing certain communication lines within the brain will create various symptoms.
When the transmission of information across the brain hemispheres is impeded in the front surface of the corpus callosum, the band of nerves that join the two hemispheres of the brain, processing of emotional content is impaired in some proportion and you will see some of the symptoms you describe (specifically the explosive temper). This has been documented primarily in cadaver studies of sports injuries, where scars too small to be seen in MRI scans have been identified and implicated in behavior changes.
Using a data processing analogy, when emotions are not processed "normally", the section of the brain "having" emotions reaches a peak processing capacity, but the section "experiencing" emotions does not receive the signals. By design, when emotional content reaches a threshold of intensity, processing is transitioned from the normal emotional processes to another section of the brain, as a fight or flight scenario.
To an outside observer, the person shows no signs of irritation until the processing shifts to fight or flight, at which point it presents as a sudden violent reaction. Once processing is shifted to the fight or flight centers, it is not possible to reason with the person.
In my own case, a brain injury, there is a physical disconnect between the brain segments, so medications will not help. No amount of drugs can restore dead tissue to a functional state.
Other people, with purely metabolic issues affecting the communication channels, can sometimes be helped with medication. Medication for them is like glasses for me. A close friend of mine with ADHD shares many of my symptoms, but he is greatly helped by some medications because his issue is metabolic rather than mechanical.
Peeing on thinbgs is a typical territorial marking behavior in mammals. While (thankfully) neither of us has any desire to pee on things, I have observed that both the friend that I mentioned and I tend to react to perceived territorial violations, to the extent that framing situations in terms of territory rather than behavior helps to establish limits and defuse many situations.
Unfortunately, the types of tests that might be helpful do not have a sufficiently high resolution (yet) to determine root causes, let alone a course of treatment. Doctors are still, for the most part, working blind when it comes to complex issues with brain function.
These journal links discuss connections between brain trauma, behavioral issues, and (to much a lesser extent) ADHD, reflecting the direction of my my personal interest.
This link is very informative and possibly useful to you. I use it cautiously because I feel the presenter sometimes borders on quackery, but he is a recognized pioneer in the use of functional bran scans in psychiatry, the content about his experience treating his nephew may be especially pertinent to your situation, and in this presentation he sticks to verifiable facts.