As DPOA for my Mom, how do I best manage her finances from afar while she lives with another sibling?

Definitely put all bills for mom on autopay. This makes much less work for you, and it creates a paper trail. Depending on how lawyer says to make money available to sis, you can autopay directly into sis’s account or another account every week or month on a certain day until you decide to terminate or change the arrangement. Sis would have no direct access to any of mom’s funds that you manage.

Records of all of this remain online with the bank for years.

Your profile says you are local to your Mom and sister. I'm in MN and my Aunt is in FL, tended to by 2 family caregivers. I have almost everything on auto BillPay from her checking account, ACH payments for utilities, and purchase as many essentials on Amazon.com (which gets paid from her own cc or bank account) and Instacart (for grocery delivery) as possible.

I agree you should have a contract with the sister, but how old is she? If your Mom is 85... (and incontinent, besides other health issues)? Is she physically -- as well as cognitively -- able to take on this task? Is she expected to drive your Mother places? To clean the house? To accompany her to medical appointments (and remember what was instructed or will you be doing this)? Would she know what to do in an emergency? Does she have any tech skills at all (like using a laptop or smartphone, texting, even a flip phone, etc)?

If she's expected to be "on call" 24/7 in the home, the sister won't have a life and this won't be good for her, at all -- unless you are planning to cover some of those hours every day.

FYI paying the sister makes her an employee and this means you will need to know the employment and labor rules for that state. Or, a contractor, and she would then need to know what she's doing regarding reporting her income. You may need to create a W2 at the end of the year for her and do tax withholding on her paychecks, which would require the help of a bookkeeping firm (of which there are many online).

If you aren't going to be the support help, you may want to consider paying a 2nd aid to give the sister some relief so she doesn't burn out.

More info on your daily role would be helpful.

I’m confused. Why do you believe that is best for your mom (with dementia)to live with your sister? A sister who is not familiar with the Ins and outs and what is and is not appropriate to spend money on? Do you think your sister will be able to care for your somewhat incapacitated mom adequately?

I would attend an elder law attorney (which is paid for by your POA out of your mom's funds) and make a care contract for shared living costs. ) Yes, that would be a monthly amount to your sister and should help with mortgage, bills and etc. and for her time, her care, her taking to appointments, and etc. Any large extras like modifications, medical costs are seperate and paid for BY YOU as POA. Billed to your mother as her bills and paid by you as her POA.

Unless your sister is pretty incapable overall, in which case she cannot do this, you should be fine.
See an elder law attorney with sis at your convenience. You are going to be traveling a bit to her and Mom now, so you can see an attorney in her area if you choose. You will pay for and get good advice. This is part of your fiduciary responsibilities to your mom, and to your sister while she is caretaker. You and sister need to REASSESS and RE-evaluate how long she will intend to do this as it goes on. What you feel about it now is subject to change, especially on her part..