Hi V.,
The best gift you can give your sister is yourself. Write her a letter. Say what you said here. Tell her how you pain for her and how you respect what she did for your mom. Tell her you want to now be of assistance to her.
Plan some special time for the two of you together. This time should be all about her. Leave any of your unresolved baggage at the door. A gift is given purely without any expectation of reward. The reward is the satisfaction of comforting another human being. In your case, the reward may be the reestablishing of a relationship. A relationship that you may have to say goodbye to soon.
If there are unresolved issues. Forgive your sister. (I say this simply because that is what is should be) When you ask God for forgiveness, he does, simply and completely. There are no strings attached. Your forgiveness should be the same. Your sister is not perfect and neither are you. I don't know if there are reasons the two of you are not close, but honestly, if there are, let them go. Love her for her humanity in all it's imperfection.
Your sister's illness is an opportunity to love and be loved. What else is there?
J. L.