Valiendo madres is a very common Mexican slang phrase that literally translates to "worth mothers" but means something closer to "screwing around," "not caring," or "going to hell."
In the song, the artist sings, "Ando valiendo madres," which conveys a feeling of being completely lost, not caring about anything, or that things are going very badly for him after a breakup. It's a raw and expressive phrase that captures the emotional turmoil of the lyrics.
The whole song is one man arguing with himself. He starts by conceding the facts, "Mija, yo lo sé, que lo nuestro acabó" (Girl, I know that what we had is over), and then spends the rest of the song proving he has not accepted a word of it. He promises to behave: "Te respetaré, no te seré loco" (I will respect you, I won't act crazy). He insists he is fine, then finishes the same sentence with the truth: "Yo estaré muy bien, y por dentro roto" (I'll be just fine, and broken on the inside).
The chorus is the best line in the song and it is barely a joke. "Nunca he llorado por nadie" (I have never cried for anyone), he says, "Ni cuando mi perro se murió" (not even when my dog died), which is the sort of thing you say to sound tough. The very next line gives him away: "Ando valiendo madres" (I'm a complete mess). Months go by, he tries someone new, and nothing happens: "A otra conocí, pero, la neta, no late" (I met another, but honestly, my heart's not in it). What is left is the same weather every time the chorus comes back around, "me rodea una nube gris" (a grey cloud surrounds me).