How do I express the notion of "drama" in Chinese?
There are different kinds of drama, for example, 悬疑剧, 推理剧, 感情剧, 伦理剧. What you wanted to express is a specific kind of drama --

活剧 - Live drama


诙谐有趣而类似戏剧情节的真实事件 - humorous and interesting real events that resemble drama plots

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闹剧 - Farce



一种喜剧; 2. 比喻滑稽夸张的事情 - 1. a comedy; 2. a metaphor of comically exaggerated event



Every day I come home to some drama. - 天天在家等着我的是一场又一场的活剧

I'm sick of all this drama. - 我再也受不了这些没完没了的闹剧

川普的整个总统任期就是一场活剧/闹剧- Trump’s entire presidency is a live drama/farce


Side note:
In Cantonese, there's a term 六國大封相 (an extravagant Chinese Opera title - a metaphor of chaotic, confrontational, or even violent scene). It may be a suitable choice in some contexts. Example: 成日六國大封相 (huge drama all day and every day)