Hey,
You definitely should tell the story.
It shows your quality of dealing with unwanted situations and not giving up.
I was reluctant to tell my story of depress and anxiety and how it affected my scores but I am glad I did and interviewer was very receptive, understanding and supportive (got an admit also).
Edited:
I believe there is more story to it then just parents being suicidal.
You could write an essay about what was the problem, how did you figure out, how it affected you, what did you learn and how you evolved and how it affected your emotional intelligence and gave you a different person about life.
The essay can be for the questions “ Changes yiu brought in people’s life”, “how did you evolve or most proud of” etc…
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