Can my mom have one daughter in charge of her finances and the other in charge of her medical? How do we set this up legally? State of MI.

My mother appointed one brother financial POA and all three of us were her Health Care proxies.

It worked okay. My youngest brother who lived at a distance and who is WAY younger always deferred to us.

I generally deferred to my POA brother if he had a strong opinion about a health matter because he and his wife lived closest, did the heavy lifting with regards to visiting and the like and because he and mom shared strong religious beliefs.

You can share the responsibility, but I wouldn't recommend it. I shared with my brother, and it was virtually impossible for us to agree on what level of care my mother needed. As he was responsible for finances, he didn't want to pay for the level of care she needed. I live close so would have had to provide the care he wasn't prepared to pay for.
Ultimately, she very quickly ended up in a nursing home. Even then, it was difficult to get bills paid. He ended up resigning as it was taking both of us too much time and energy to get anything done.
I will never make my kids share this "responsibility" as it will just end up with them fighting. Instead, I will make my wishes crystal clear, including all medical directives and ask one of them to just adhere to that.

This is possible in a guardianship situation, possibly depending on the state. In my state (East coast, small), my sister and I were named co-guardians of our mother. I handled the finances, sister handled medical appointments, as these roles suited our individual skillsets. It worked passably. We got along really well, mostly trusted each other to do the right thing, and kept each other updated frequently. I made sure sister never felt in the dark about the finances. She got copies of all bank statements, etc., so she would never have to worry about me abusing my authority. In matters of placement, we worked together in researching the places. I would provide the financials, she would provide the medical history.

It's not easy becoming guardian, though. It took months in the courts, and in the low five figures in legal fees when all was said and done (our case was a bit complicated). I wouldn't do it over again—I thought we should have let the state handle it, and I wish I had stuck to my guns—but it did bring my sister and me much closer together. Then mom died, then sister died a year later, and I am grateful that she and I reconnected like we did, for the little time that we did.

I've shared responsibilities as POA but will never do it again. It is true that if there are joint POAs some of the work is shared (notice I said "some"). The problem is getting two people to agree on many things over what could be a really long time.

What is preferable, if "help" is truly needed, and sometimes it isn't, is that Sister Sadie is DPOA and Sister Sheila helps her with duties, such as taking deposits to the bank or doing the grunt work to get a new cable company because the old one isn't working for dear mom. However, usually Sadie is DPOA and Sheila never offers to do anything or she can't because she has a "real job" as opposed to caregiving, which isn't a "real job." So Sadie is not only taking care of finances but dealing with every little practical thing that comes up, like hiring the sitter to stay with mom so she can run out and buy mom a new pair of shoes because mom's just lost a sole and mom can't get along without her shoes, the ones with the fuzzy lining, which are nowhere to be found in any local store, so Sadie goes home, pays and dismisses the sitter, and goes online to find the shoes, but Sadie has to cook dinner and eat it with mom, who is complaining that her feet hurt and where are her shoes? Meanwhile, Sheila is out with friends at a male strip club, completely unaware that Sadie is having a problem today.

The answer to your question is obviously yes, one can be in charge of finances and one in charge of medical. But don't expect it to run smoothly.

What happens if MPOA, your sister, decides to stop treatment of mom's illness so she can die in peace, and you say you want her to go on living each precious day? (In pain, but no matter, it's the philosophy that is relevant).

In many cases, one person is assigned for all positions. IN our case, DH is his mother's POA over everything.

However, his sister really holds the reins. He's FINE with that b/c it's something he is not comfortable with. YS does keep him in the loop, I think. Although I have been shocked at the things he should know and doesn't bother to ask about. Well, not my circus, not my monkey.

For DH and myself--our oldest daughter is POA with the co-POA being our 3rd child, also a daughter. My son may be an attorney, but he is such a PITA, I can't in good conscience put him charge of anything. Also, he lives 800 miles away. DD's are both local--and both very organized and efficient. I have no worries that they will handle things just the way we've asked.

And yes, this is in our will.

If your choices for split POA's do not get along--think long and hard about appointing them to the jobs. There is a lot of mind-numbing work that goes with disposing a will. I've seen many a family fracture into nothingness b/c the POA's don't agree.

It almost always causes bickering, if you have long been here reading. I think it is a very bad idea. I would choose the person best at record keeping, with most time to do it, and make the other a "second". What can possibly be gained by putting two people in charge who will almost certainly not agree on all aspects of everything? What possible advantage is there?

See the lawyer who made up the original. As said its unusual that the Financial is done and not the medical. It would be nice if you work together but we have seen on this forum when the financial POA and the Medical do not work together. As POAs, you do not need to share info with each other. I would make sure there is a clause that the principle wants both POAs to share info with each other. Its really not recommended to have 2 separate people hold POAs.

For me, my one daughter is good with money matters. The other is a Nurse so I will be splitting the responsibilities of my POAs.

There are 2 different POA's required. One is the durable or DPOA, which handles all the financial decisions, and the other is the medical POA, which obviously handles all medical decisions.
So yes, mom can have you as her DPOA, and your sister as her medical POA.
Again they are 2 different POA's, so if you're already the DPOA, then she just needs to have the medical one done for your sister, although I've never heard of an attorney only doing one POA and not the other. Something doesn't sound quite right here. I would double check moms paperwork from her attorneys office, as I'm guessing that both have already been done.
And if not, perhaps you can clarify as to why they weren't both done together.

Your Mom has to set this up through a certified elder law attorney. She should also create a Advance Healthcare Directive, so that her MPoA doesn't have to second-guess what medical care she gets (or doesn't) if her health takes a more serious turn and she becomes too incapacitated to state her desires for end of life medical treatment.

My MIL has 2 of her 3 sons as her PoAs, sharing the same responsibilities. Fortunately, they work together well and their Mom's needs are not complicated. You never know what will cause a rift in agreement or cooperation, so maybe ask this question to the elder law attorney, since they've mostly seen it all.