malovitt is right, once the POA is active, i.e. the cared-for person has been declared to lack capacity to make their own decisions, then the cared-for person also lacks capacity to make a will.
However, you can set up a POA at any time and it is not activated until you lack capacity - as certified by a doctor.
Please everyone, do set up your POA and write your will while you are able to do so. You will have so much more choice about who is in control of your lifestyle and finances.
There are two types of POA - welfare and continuing (financial) and separate people can be appointed for each if you wish.
OP sorry to hijack your thread.
Your sister is of course being unreasonable. It is uncomfortable for your mother to be in clothes that are too tight, she shouldn't have to wait over a month to be comfortable - that could be seen as abusive.
Do go over the POA with your sister and make sure your sister knows that you will quite happily apply to have her removed if your mum's interests are not put first.