Some people are more conscious of their own behaviour and can accept their own issues, some people, like your mother perhaps, don't realise or accept that they are stressed and they are channelling that energy into the wrong place, ie you.
You are aware and accepting of the stresses that each of you has, especially your mum's. Therefore you are the stronger one, so know that your mum's behaviour is explained (although not justified) by the stress she is going through. She is not dealing with it in the right way, but forgive her because she is not aware of that fact right now.
As for your own stress, I think it is unwise to seek help from another stressed person as both of you will try to override each other's emotions with your own, because they both will be very intense. It will end up helping neither of you. When you are stressed, do not go to your mum, go to someone who is outwith your situation, but still knows what is going on.
I also think that there are other issues you have which you must deal with, and they are surfacing now because you are in a time of high emotional strain.
There are organisations which can help cancer patients and their families emotionally, your dad's doctor or hospital will be able to give you more information on this. You can speak to them individually or as a family. If there is tension between other members of the family and not just you+mum then go for the family session.
I wish you all the best, and hope you can resolve everything.
Z x