Chrono Trigger has a lot of side quests and character development arcs, and multiple endings.
I believe this particular event becomes available after you rescue Chrono from Lavos. During this period, you can do all kinds of different adventures, like the Mother Brain Quest for Robo, and getting cool gear from quests like the Rainbow Shell.
Anyway, to start this "quest" (I wouldn't exactly call it a quest - it's more of a cutscene), all you have to do is visit Guardia Castle in 1,000 AD, the only requirement is that you must have Marle in your party for this to happen.
Chancellor: I've been worried, Princess! I understand your pain. But the king really only cares about his realm... Yes, even when your mother, Queen Aliza passed away, he worked all day!
Marle: No one could do that! It's inhuman!
Chancellor: Oh, child, it's ancient history now...
Marle: Tell me more!
Chancellor: This may be difficult... Well, Queen Aliza's condition suddenly changed for the worst. She desperately wanted to see the king one last time, but he couldn't find the time to drop by... Said he had some work to do... But knowing nothing about death, you waited faithfully by your mother's side... Aliza passed away in sorrow... It's as if the king indirectly killed her... such a shame...
Marle: WHAT...!! Father KILLED?... MY MOTHER...?!!
Chancellor: But what do I know! There are reasons for everything, right dear? Now... so glad to see you back again. Please go and visit the king.
It's been a while since I've played, but I believe this is prior to doing the Rainbow Shell quest - as that involves the King and Marle again, with a very different interaction between them.