I'm really struck by MyChien's post which I think is very insightful. Probably the most painful part of my mother becoming suddenly very ill and then very disabled has been the appalling clashes between me and my siblings - even though she's been so unwell that she has been in first a hospital and then a nursing home throughout. We are finding the distortions of our childhood roles and relationships keep tripping us up - even though we're all getting on for 60!
So I'd also support you getting counselling or therapy in some way. Caring for someone with dementia or even minor cognitive decline is HARD. I do think that part of your reaction is disappointment that your brother is not seeing what you want without asking. In my experience as a health professional, the invisible majority ethnic culture in Britain (which you may or may not be part of) is that help is supposed to be given without being directly asked for. That being pushed to the point of having to ask directly for help is an insult, and frankly almost a personal failure. So you are not asking for help. And your brother is not helping, but criticising, and that's unbelievably painful. I wonder though if he is somehow asking for help himself in a very dysfunctional way. (that doesn't mean you have to spend lots of energy finding out). Our culture is so difficult to negotiate in these circumstances.
I do think that getting professional help with your current circumstances is an obvious way to reduce the burden on you. If you take your father's direct request (are you going to leave me? Please don't leave me) as a face-value statement both of what he wants and what you need to do 100% of the time, you are going to collapse. You need to interpret that in a realistic way. That cannot mean that you can't take a break, can't take a holiday, can't involve other people. Remember that he could get to know strangers - they could become people he knows. Would it be terrible if he had a person he knows stay with him for a week while you go on the course?