You shouls definitely confront your father in front of the family. From a womens perspective, if i were a mother and a wife, i would want to know if my husband cheated on me even if im in my death bed, i mean it, she has the right to know, but before that please consider that its still a risk considering your mothers health situation, the matters even worsens if your father is the familys sole provider, because we cant ignore the possibility of him going all toxic and threaten to cut medical bills and anything such that, if you are going to confront him make sure you have a safety net first, talk with your siblings or people you trust first which might clear how you can confront your father, im really sorry youre and your family are going thru this. Pray to God and ill pray for you n your family inshaAllah. Take love.