ghItlhpu' ter'eS, jatlh:
> Why not just {muvmoH}, then? What does {-chuq} add to it? "Cause to
> unite" v. "cause to unite each other"?

You're just relying too heavily on the English gloss there, that's all. {muv} means not "unite", but "join": it's {muvchuq} that means "unite" (literally, "join each other").

QeS 'utlh