I am so sorry your family is torn apart and it seems to go back years. I of course will pray for your sister. You mentioned your Mother caused much of the dissent in your family and from what I sense she is still in the middle telling each of you what the other said. Perhaps it is time to bypass Mom and talk directly to your sisters.
It may be just Mom they want to avoid and would jump at the chance to mend fences and get to know you as an adult.
For your sister with the Cancer, I would send her a card and ask if it would be alright for you to visit her and that you will surely repect her wishes. That of course is if you feel you want to reach out to her.
Gentle hugs sweet lady. One foot in front of the other will get you there.Kitt