If you live in the UK or their territories it sounds right. I call women and girls sweetheart. To me it means nothing more that respect and kindness. I am a public servant, and am required to be polite. In 12 years, I was told not to by one crabby old lady with her own issues.
Tread carefully when you start sniffing around ex's family members with 'those' kinds of intentions .. although you have distanced yourself from your ex, you are messing the family.
It may very well be that she cares for you .. and there's nothing wrong with that. But, in all fairness and respect for her sister, I wouldn't encourage a rift between sisters if I were you. After you are long gone .. the rift will still remain.