The hard truth is that you can't force your mom to complete a power of attorney for finances if she refuses to do it. But there are other practical steps
you can take to curtail her access to her own funds"”and it sounds as if you and your sister have already started that process.
The more you can get the banking records automated and out of your mother's reckoning, the better it may be. Look into whether it's possible to arrange for more automatic deposits, to monitor any accounts with online access, to have the bank send automatic phone or mail alerts to you or your sister if there are withdrawals over a certain amount. Sometimes these solutions don't follow established procedures, but an understanding and creative bank manager may be able to help craft workable solutions.
Also, perhaps there is a way to find out your mom's current prime concerns about money and address them"”at least for a while. If she fears not having cash on hand, for example, you might dole out a weekly amount like an allowance. If her concern is not being able to pay bills, you might simply assure her they are paid in a new way. If she yearns for more material things, you may be able to distract her fairly easily by concentrating her attention on some of the things she already owns.
There is also the possibility that your mother's condition will worsen in the future to the point that you, your sister, and other concerned individuals may want to consider an adult guardianship or conservatorship for her. Such arrangements, which would not require her consent, would allow for another person to manage and control your mom's finances on her behalf. For more information on this, see Caring.com's section on guardianships and conservatorships at www.caring.com/adult-guardianship.