I don't find this story credible.
First, why in the world does the kid give up and kill himself after a few weeks on his own? He works at one job for a few weeks, gets fired, and kills himself? That is not plausible to me at all.
Second, your father is a businessman, and he cannot comprehend an employer firing a slacker kid after two weeks on the job? I've fired half a dozen people before their probation period is up, because I determined they were incapable of their job, misrepresented themselves on their resume or in their interview, or weren't getting along with their coworkers. It makes zero sense for a seasoned businessman to blame another businessman for firing his son from an entry level job.
You would need a far more actively evil employer and much more time for him to stress out the kid to warrant any sort of blame. And "irrational grief" is not a get-out-of-jail-free card that lets you just do anything and claim anything you want; readers have to get it.
Further, I don't buy the empathetic hired killer angle. Hired killers do the job or they don't get paid, and they aren't psychiatric counselors. Most people given as the target of hired killers are innocents (witnesses, prosecutors or other public servants in the way, wives or husbands or others standing in the way of an inheritance, sometimes politicians trying to do their job, or just in general a non-criminal obstacle to something a criminal wants). Nobody becomes a hired killer if they aren't willing to kill innocent people, and that requires a distinct lack of empathy. (I would make a distinction between a hired killer and a soldier sniper that kills the enemy or assassinates enemy soldiers or politicians -- enemy combatants and leaders are not innocent people -- but that distinction does not apply here.)
I do not find it plausible a stranger talks a father out of a grief that has been going on for months. To make this father bent on revenge for that long, you must vastly increase the culpability of the other businessman in the death of his son, and that must go on for a much longer time. However the other businessman abused or coerced the son and drove him to suicide, must come to light to the father, so his anger grows as he investigates more. But that in turn makes the plausibility of him being talked down and abandoning his revenge very implausible.
Sorry for the negative answer. I am trying to save you time, a storyline has to be plausible to the readers, and I think you are taking far too much liberty with the irrationality of grief, blaming a two-week employer, and a son committing suicide after failing at a few weeks of work.
As a start, I'd suggest you get this son killed on the job and make his employer a criminal that intentionally sent the naive son into lethal danger. Then the father, investigating the circumstances of his son's death, has a good reason to want to seek revenge against this guy. But that still wouldn't fix the implausible hit man with a heart of gold, or a stranger talking the father into letting the employer off the hook.
Edit: The OP comments he could make the son murdered, and the murder made to look like a suicide.
In that case, the last paragraph above applies. The father can know his son would not commit suicide; in fact an early scene between father and son can seal the deal:
Son was angry. "That's it? I'm cut off forever. With no warning."
Father shook his head. "I've told you a hundred times, son, you cannot party forever. But you are my son, you will always have a bed to sleep in and food to eat. Doctors if you need it. But no more money. No parties. No more cars, the next one you wreck will be one you paid for yourself. No more half naked women parading through my house. If you want entertainment, get a job and pay for it yourself. Or watch TV, I'll give you that free."
"How is that different than a prison sentence? No thank you. Screw you. You think I don't know how to make my own money? Screw you."
Then the father knows the son did not have anything "real" to despair over, and would not have committed suicide. Father could still be paying Son's phone bill, for example, considering that a basic need, so Son could always pick up the phone and call him for a rescue. But upon investigation, Father can still feel guilty for not anticipating his son would get involved with a covert criminal enterprise to make money, and perhaps Son saw something he shouldn't have, and his suicide was forced, yes he was hung, but did not hang himself. A real medical examiner finds bruising on the body suggesting a fight minutes before he died, or something.
Now the father has reason to investigate, and hire people willing to be violent to counter this covert criminality and take revenge. You still have problems, the hit man with a heart of gold makes no sense. But your character for that role could be somebody the father hires to protect himself after the covert criminals make an attempt on his life. It is implausible a stranger could talk the father down from revenge, but somebody that has saved his life and become his friend, and shows him how he will destroy himself, his daughter, and perhaps sacrifice his own innocent workers in the crossfire, might be able to talk him down from his rage. Then for a satisfying ending, the same MC-bodyguard military sniper covertly kills the criminal and the henchmen that killed Son.
In the reader's eyes this will not be murder, but justice. Without fanfare. Father can learn of these deaths, and the MC can deny any knowledge of it.
"Karma," he tells the Father. "They live by the gun, they die by the gun."
But then the MC bodyguard is no longer needed by Father, it is time for him to move on. Next adventure. You have a story.
