Once you have POA you need to be careful to keep her finances separate. Its not just relatives who might ask to see accounting. If social services or the tax authorities felt that assets were being diverted, they might well take action.
Is the joint bank account essentially your mother's money, which your sister has access to? If so this is easily sorted. Speak to the bank, and I suspect the best approach is to convert it to an account in your mother's name with a third party mandate for your sister. When the POA comes through you register this with the bank, they then cancel the third party mandate and replace it with POA access.
If it is shared money your sister will need to sort this out. The POA takes about 3 months to come through so plenty of time. A separate account should be set up in your mother's name, and any money and income streams which clearly belong to her should be transferred. The first account should then become your sister's account only.
(As long as decisions are justifiable there is advantage in having money in your sister's rather than your mother's name. On one end of the scale because of IHT, but on the other because Social Services care, which your mother will probably have to contribute to, can be limited. For example it took a while for the community physio my mother needed following a fall to gear up, and so private physio helped get her moving. Or simply money for small luxuries such as toiletries.)
The POA should be a chance to discuss how you manage things between you. A lot of the finance stuff can be done long distance, so depending on aptitude, you might have the further away sister do the finance stuff whilst the closer sister does the more hands on support. In terms of POAs the natural instinct is to share decision making. However it is much easier to have a single Attorney for the Finance side, with an alternate should anything happen. Banks prefer it. If there are a lot of assets/income you might stipulate that the accountant who does the tax returns prepare an annual statement of income and outgoings. Care and Welfare is different and you, your sister and your mother might feel more comfortable with joint decision making.
If the financial affairs are quite complex consider including wording in the POA document that allows not only for expenses to be recharged but also for a fee to be paid. It sounds mean but firstly employing a professional would be far more expensive, but also it makes it less likely that any unequal burden is resented. OPG are helpful, but if you are in this territory use a lawyer to provide advice and help set up the POA. Once capacity is lost it is very hard to change things.