The Spanish mullir (“to soften”) comes from the Latin mollis, meaning, “soft.” From that same Latin root we get the English… to mollify. To mollify in English is usually used in the sense of, “to appease” — and it’s noteworthy that that appeasing IS softening. You need to be strong to not appease the bad guy, after all. 

The m‑ll root is clearly visible in both words.