My sibling is mentally incompetent and has dual POA. Any suggestions?

Seriously doubt you are going to get anyone who "can function as a full-time job" declared incompetent. Making what you (and even most people) consider to be bad decisions is not a sign of incompetence either. Being drunk temporarily impairs competency, but not in the overall legal sense.

You would most likely do better challenging your brother's POA based on his willingness and/or availability to serve. He is unwilling and unavailable because he is either working or drinking and hung over during his free time.

Same question as Ann. Is it actually a POA that requires you both agree to get anything done? Or is one POA and the other successor? What does the POA state what happens if one of you develops health problems told becomes incapacitated?

Dual POA always a bad idea. No family is completely in agreement all the time. There are so many dysfunctional families of caregivers on this site we recognize what a nightmare this would be.

Is mom competent? If so, she can change the POA anytime she wants. Does mom recognize the problem? Or is she in agreement with what bro does?

Your profile says mom is 54 with Alzheimer's/dementia. Is that correct?

Does your POA explicitly state that your decisions require the consent of both of you?
Can you consult the lawyer who drafted the POA to clarify the obligation(s) you have for one another.
Is he drinking now?

I would see the lawyer who wrote up the POA. I would say there needs to be a way because he is not competent. But then, how do you prove that?