ICB, your posts make me feel quite sad for you. You are allowed to enjoy BFing and get benefits from it too, you know! No mother in the world is such a martyr that if it was a godawful experience each and every time that she would carry on for years in suffering. I know that depression can make you feel selfish and undeserving, but please don't ever feel that BFing your child was or is selfish, or feel guilty for enjoying it.
If the BFing was the only 'good' times for you, then it was 100x the good times for her! Plus, all the other lovely things I know you did for her despite suffering within yourself (even if you couldn't identify them).
Please don't look down at her nursing and feel like an outsider or a freak or whatever. You know that this is a wonderful thing that BOTH of you enjoy (minus the nose-poking... it does stop, honest!) so everyone can go take take a flying jump, frankly! As you say, the majority of the world's mothers feed for longer and all the science on the subject gives you the thumbs-up, so stop worrying and keep on enjoying. And enjoying for your own sake too.
I bloody love BFing. Of course, I get benefits for it. It's not for my benefit, but I benefit from it also. I don't want to speak for others, but when other posters decry the idea of it being for their benefit, I don't think they're meaning they don't also benefit, I think they're just defending themselves against the daft accusations that mothers make older tots nurse purely for their own needs/desires/issues. Other posters, please feel free to tell me I've got you wrong, if I have.
As you know, you cannot force a child, especially an older one to BF. And it sounds like your DD wants to - she was clearly very annoyed with you for witholding it from her that day!
As Goldmandra says, you have to gently and constantly influence your baby and child. We influence them with their sleep and naps, with eating solids, with play, with behaviour and manners inside and outside the home... you name it, we influence it. The very fact that you worry about not placing undue pressure on her that are secretly your needs shows you reslly won't do! People like that man you mentioned have no self-awareness and you clearly do. I'd hate to think you might not BF your DD when she wants to because you convince yourself she want to stop because you feel really unworthy of exercising any influence on her.
You sound like you are a really caring, thoughtful and responsive mum :)