Adueña comes from the verb "adueñarse," meaning to take ownership or possession of something, often used for feelings or hearts rather than physical objects. It is a stronger, more dramatic verb than simply "tener" (to have).
In the song, the lyric "de mi corazón nadie se adueña si no me firman papel" (no one takes ownership of my heart if they don't sign my paper) uses the word to demand real commitment before anyone can claim her love.
Have you ever been so heartbroken that you just want to give up on love entirely? That's exactly what Aymée Nuviola and Mayito Rivera are singing about in "Consuélate Como Yo"! They're both commiserating over past loves that went wrong, with lines like "Ya yo no vuelvo a querer" [I'm not going to love again].
It's a really fun, relatable song where they tell each other to "Consuélate como yo" [Console yourself like me] because they've both been there. They're making a pact, saying things like "ni tú vuelves con ella, ni tú vuelves con el" [neither you go back with her, nor you go back with him]. It's a blunt, humorous take on heartbreak, declaring that they're done with lies and games, and ready to change their ways to protect their hearts!