I'm not really sure what to say...
Well firstly, your mum has absolutely no right whatsoever to moan about you wanting to go and see your dad on Christmas Day.
I think you should definitely go and see your dad, as it could be his last Christmas if he doesn't pull through the cancer.
You should talk to you mum about her not inviting him. Tell her you have a right to see both your parents on Christmas, and that Christmas is a time for "goodwill to all men" or is it man? Similarly you should tell your dad that you want to spend Christmas with him and you mum. Do you fear it may be his last? If so tell him this is what you fear.
I think you should try to pursuade him to tell your mum that he has cancer.
If you do manage to get him to come round for Christmas dinner, beg them to be civil to each other, for you and your siblings sake. And get you mum to make sure her family are civil too.
I am sorry about your dad having cancer, I hope he pulls through.