I know what you are going through, unfortunately he is just like many people with Parkinson's the disease is what is causing him to behave like this and he can't help it. This is what makes coping and living with PD so difficult he must be is so much pain with his head and neck as two of my friends who are in the same situation tell me how they feel.
The poor man must be very frightened, friends with PD including my husband tell me how their whole body feels when they can't move and that their throat, swallow, eyes and every part of their body feels absolutely dreadful. It is very common for people to think pwp's are putting it on and mostly its because they don't understand the disease, its also very hard for us carer's to understand fully, my husband has had it for going on forty years and is only seventy so we have been through lots of different stages. What you and your Mum need is a case conference to sort out his proper needs and even speak to his consultant as they may be able to give him some different drugs to help him.
Nursing homes are mainly happy for people with very little need but once you get people with PD they are not keen to have them because in their words they take up too much time!!! even though the homes charge such a lot, I feel the whole system needs looking into including how much profit the company's make.
As to the question of his needs, I would think he would be entitled to continuing care and you need to approach the home and get him assessed again. Following on from that my question to the government is are they getting a good service for all the people receiving continuing care as actually they are paying for it as are the people of this Country in their taxes.
The care system should be more professional and give a good structure for carer's to progress in a career. Where my husband is the carer's have been waiting two years for the company to start them on NVQ's whereas in the community carer's are much more likely to be at least NVQ level two trained and sometimes level three.
I hope you get some help and make some progress.