I breastfed Alyvia until she was... oh lord... 20 months? 21 months? It was just a couple of months ago that she was weaned, and she'll be 2 next month. She was extremely difficult to wean, so I can sympathize with your sister. What ended up working for us was stopping cold-turkey. It shattered Alyvia for a few days, but after a week or so she (almost) forgot completely about nursing. Every now and then she'd reach for one and cry when I'd say no, but she's grown out of that completely now.
I only nursed her in public when she was younger and relied 100% on my milk. And I had a black nursing shawl that I used. It was like a poncho I guess, but it was made out of very lightweight material. It slipped over my head and covered completely, so I never had to worry about people catching a peek, and it allowed me to nurse my child in public without offending others. And the neck of the shawl was loose-fitting, so I could look down and see her, and she could look up and see me. It's a great tool, and I plan to buy a new one for this next baby.
I would not nurse without one. That's mainly for myself though. I'm not comfortable exposing myself to others, not even family. I would either use the shawl or excuse myself and step into another room with Alyvia. I don't think I'd personally be offended if I saw a mother nursing her child in public, but I can understand if others would. Maybe they don't want their children to see nude breasts, or maybe the idea of nursing sickens them. I can understand them not wanting it shoved in their faces. And I'm not saying nursing mothers should be forced to hide it - just be respectful of others and use discretion.