Some people, especially overachievers just will never, ever "get it".

My father is like that. He has seen me at my bipolar worst. He has gotten phone calls in the middle of the night from the ICU doctor saying I might not make it til the morning and he still doesn't "get it"

BUT--it sounds like she is at least trying to and it sounds like she is interested in having a relationship with you. That is actually a LOT!
My father has no interest in EVER trying to get it nor in a relationship with me. So, at least you have that in your sister.

I'd say take it slow and keep building upon the foundation of love you two share.