@GnarleyC7, I feel for your situation, from the other side.
As the youngest of three sisters, I was the one that moved away when I was young. While my sisters still lived in the small town where we grew up, the care taking of our mother fell to them.
She was always difficult even before the dementia set in. In her case it was not Alzheimer’s but dementia brought on from hardened arteries.
I lived on the other side of the country and did not have the means to come back to take care of her. I know my sisters understood that but I felt guilty they did all of her care.
You mentioned your sisters do not help. Do they live near your parent? Also have you asked for their help? If not can you ask for help? Is it possible they just do not understand what is needed?
My suggestion would be to have a “family meeting” of some type. Not the finger pointing type, just a discussion regarding how much care giving takes, the expense as well as the stress it may cause. Tell them no arguments allowed, simply a discussion on how you need assistance.
Is a long term facility a possibility for the situation? Many times this is more positive for everyone involved.
I know how difficult it can be but I worked in a facility that did wonders for families. Is there anything in the trust for this situation?
I understand the time and cost of caring for an aging parent and know it puts a strain on family.
I guess I took the long way of saying, talk to your sisters about it without pointing fingers or flack from either side. It may be they do not understand what it takes. A long term care facility is not abandoning a loved one and if your sisters are unwilling to help that would be a great way to handle your situation.
Good Luck and I hope you find answers that help.