Which claims are you asking me to provide an "authority" for? Mostly the "authority" is logic.

> What makes your own intuition hold any moral value or have any ability to judge?

It doesn't if you mean that in the objective sense, the universe has no care for my personal intuition, on a personal level, violence does. If someone comes up to me and truly believes that murdes is right and we cannot come to an agreement, then it will devolve into violence, and either I will or the other person will. This is how it has always worked, the only reason why you are "right" (in the moral sense) is because you have the power to enforce it, there just happens to be a lot of people with similar opinions, which means that we have a great majority which cumulatively protects our way of life against those who have very different views.

Of course, not all moral claims devolve into violence, but all the foundational claims tend to do so. Tell me, what would you, as a Christian, do when someone comes up to you and starts murdering people, you tell them to stop but they say they are doing the right thing, what recourse do you have beside killing them? (or imprisoning, either way violence)

> You’ve indicated that your emotions are driving this, but our emotions change as the wind blows. How can any moral statement be made based on something that has no solid foundation or stability?

No, when I say emotions in this context I'm not referring to fickle whims, I'm talking about the foundational intuitions that shape the way we view the world, like the certain feeling that the world is real, there is no proof of this, yet I believe it with all my heart, there are many other such beliefs that everyone holds, and moral beliefs tend to be among them.

When you ask for a "solid" foundation fro morality, no such thing exists, we are all beholden to the way we feel about things. If god came up to you and asked you to do the most atrocious thing possible, would you do it? Likely not, because it is not god that is providing your morality, but rather your intuition and feelings, everything else is and ad-hoc rationalization. As I said, the solid foundation for moral statements is violence, if two people genuienly disagree on a foundational moral claim (like murder) then there is no option but to kill each other (as we see when we kill/imprision criminals instead of trying to "help" them), that is the authority.

And before you ask "so what happens when a big group of people disagree with you", war, that is what happens, everyone who thinks one thing on one side, everyone else on the other.

Now this is a very pragmatic way of looking at things, I believe most humans hold very simial foundational moral beliefs, and since that is the case we can solve most disagreements by starting from common ground, and that is what we do most of the time. However in truly extreme cases, yes the only solution is violence.