Metiche is a popular and very useful slang word in many Spanish-speaking countries for a person who is "nosy" or "meddlesome". It's the perfect word to describe someone who butts into affairs that are not their business.
In the song, Romeo Santos hilariously complains that the problem in his relationship is his girlfriend's mother, calling her a "maldita madre de metiche y bochinchera" (a damn nosy and gossipy mother). This single, punchy word sets the entire comedic and dramatic tone of the song.
Romeo Santos tackles the age-old trope of the nightmare mother-in-law in "Suegra", and he doesn't hold back. Instead of blaming marital friction on lockdown fatigue, he calls out the real culprit: "No fue efecto de cuarentena / Era tu maldita madre de metiche y bochinchera" ("It wasn't an effect of quarantine / It was your damn mother being nosy and a troublemaker"). The Dominican slang is brilliant here: bochinchera is someone who lives to spread gossip and stir up drama, while revolú describes the absolute chaotic mess she leaves behind. He gave her a place to stay, and in return, she seems dead set on driving his partner to file for divorce. He even jokes that she has a degree in ruining his life: "tiene un doctorado en joderme" ("she has a doctorate in screwing with me").
Things cross into hilarious, theatrical melodrama when he starts plotting her demise. Romeo sings about giving her a sinister birthday gift: "Un buen cafecito, pero envenenado" ("A nice little coffee, but poisoned"), followed by loading her into his car and tossing it off a cliff—"de una barranca pa'bajo, se la lleva el diablo" ("down a ravine, the devil takes her"). It is completely over the top, set against crisp bachata guitar grooves. You end up sympathizing with the poor guy while laughing at how wild his frustration gets.