It is a really difficult situation that you are in - I am having similar conversations with my own parents for different reasons while looking into this for myself as well because I also have Parkinson’s Disease. Life is certainly not simple.
This is the government guide that you will need to read:
I’m no legal expert and this is tricky stuff but I think I’m correct in saying that you can’t make a lasting power of attorney for somebody else - the person it applies to has to make it for themselves. They can have help but have to be able to understand the process and make their own decisions and if this is not the case then the document would not be accepted.
Each LPA costs £82 to register ( or maybe it’s £84). For somebody looking at a social/healthcare and also a financial LPA that is over £160. I am currently saving to be able to put these in place. I don’t know if you get a refund if you get something wrong or it isn’t accepted so I would seek advice before applying for anything if you have any concerns that it will be rejected.
As well as the links you have already been given, which I would definitely check out, Age UK have a good section on LPAs which might be worth a read.
Hoping you get some support with this and get to where you need to be, Jx