Is there a way to find out if an irrevocable contract has already been arranged?

Unfortunately, you are in a difficult situation. You want to know if your brother has already made an irrevocable contract for your mother with a funeral home. Clearly, it's important See also:
Is it true that an irrevocable trust does not take effect for five years? that you learn the answer to that question. But your brother won't tell you if he has or not.

I doubt if the state of Michigan can provide you with the answer to your question, because I doubt if there is any law or rule in Michigan that would require irrevocable funeral contracts to be registered with some central agency. But I am not an expert in Michigan funeral law, so there's at least a theoretical possibility that Michigan has some unusual practice that requires central recording of these contracts. All I can suggest is that you do a Google search, starting with "Michigan, funeral homes, irrevocable contracts," and see what you can find.

Perhaps you could suggest to your brother that having two irrevocable funeral contracts would not be in your mother's interest at all, so on her behalf he can tell you if he's already made one.