Moral relativism is about handling the disparity of moral frameworks in the world, which you acknowledge exists at several points. The inverse of moral relativism is moral absolutism, which is that there exists precisely one set of moral facts. The space between these two is a spectrum, by the way, and usually we choose our position on the spectrum depending on what our purposes are. If we're talking about a disparate cultural collective, moral relativism is structurally necessary. Relativism just means we have a contextual differentiator, just generally in philosophy, not just in moral studies.
The struggle you have with pinning down moral relativism I think betrays the fact that your understanding of it is low quality. A good ear mark is, can you name a single passage from a treatise on moral relativism that you like? If you can't find a single aspect of a philosophical construction to advocate for, that means you don't actually understand it.
You also keep sliding between conflating moral relativism with moral anti-realism and even moral nihilism at one point. These are different axes.
> Realism + Absolutism
All moral facts converge for every single person. As a matter of fact, they aren't facts at all. Morals are a hinge of the Wittgenstein variety.
> Realism + Relativism
Moral facts are derived from frameworks, or contexts, which are themselves grounded facets of reality.
> Anti-Realism + Absolutism
Kantian Constructivism. There are no facts which are coherent without a framework, but moral claims are still necessarily only capable of being universal.
> Anti-Realism + Relativism
Moral reality is constructed by the framework, grounded only to the framework.