My deepest condolences, gillybob, to you and your family. It's hard to lose a mother, no matter how old we are.
So sorry that your mother suffered for so long, also. She sounds like a very brave woman.
I agree w/ the poster who said to be kind to yourself. What did your mother mean when she asked you to "look after" your dad? Is he ill, too? Or was she asking you to cook and clean for him (hopefully, he has learned to do some of that for himself, while she was ill)?Or did she just mean for you to check on him, now and then, and see that he's ok?
Please don't let her request weigh on you too much. As I'm sure you know, you and your sister can't replace her - you're not supposed to - you've got your own lives to live. If he needs care, please don't hesitate to reach out for professional help - whatever he needs - a nurse, a HV, a cleaning lady (I realize some of this may be prohibitive financially). The point is, once again, be good to yourself, even as you're trying to help your father.
For now, I hope you, your dad and your sister will all pull together and see each other through this.. Peace to you...