I am so sorry, you have so much to cope with and it must be very difficult . you will find lots of support on here. My first stop would be the Hospice because they have all the services you will need under one roof for now and they will help you get through - at least that was my experience when my husband had lung cancer and my mum had memory loss. They helped accelerate his attendance allowance on limited life expectancy grounds, they directed us to other services, they had some day services avaailable there and arranged transport, they had hospice at home if you wanted to access that.
They should both be getting non-means tested attendance allowance
my next stop would be social services probably to get a carers assessment and some free 'sitting hours' to give you some peace of mind as you are caring for them both. Social services can also help you to access some day care for your mum to give your dad some rest.
There is a lot more info but probs too much in one go. It is difficult when you have two really serious problems (like you I had two young teenagers as well so i understand how difficult the juggling is but we all get by!!!). Keep posting, lots of friendships and support on here xx