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.