I know this is probably not what you want to hear, but it is quite normal for children to breastfeed until they are older...it is quite normal for most children in other countries to nurse into preschool years. I nursed my son until he was ready to give it up at 29 months, and he gradually needed it less and less which made the weaning process quite smooth and effort less. It sounds like your daughter is fairly high needs and she would benefit from a similar approach. Attempts to wean, esp the cold turkey approach may have just made her more attached ....she feels she deperately needs to maintain this since she feels it has been taken away.
If you want to move more towards weaning, the best approach really is don't offer, don't refuse. If you really don't want to nurse at the moment she wants to, try to distract her with something else she really enjoys. Often kids will forget then that they wanted to nurse. Or, if she is old enough to understand, tell her not right now, or can you wait a minute and put her off as long as you can...this will increase the time between feedings and generally cut down on them.
Nursing before naps is not a bad thing. I would see if she might possibly be willing to nurse only before sleeping. That way she still has that source of comfort when she needs it most to relax etc. She will grow out of it on her own, and there is nothing harmful to her nursing till she is a little older. If anything, it is beneficial in that all that wonderful nutrition and antibodies that she got when she was a tiny baby, she is still getting and she is learning to be confident and more self sufficient when she knows she can rely on you when she needs you. The more she gets the message from you that you will be there when she needs you, the more confident and independent she will grow to be. I know nursing can be extremely draining on you...and it is hard to juggle your needs vs. her needs, but from what you say it really sounds to me at least, like she needs a little bit more. I am sorry, it does sound like a tough situation....unfortunately some people are blessed with more needy babies than others.
Who cares about judgemental stares? I know it always effects you at some level, but they cannot really judge. They do now know your daughter, they do not know your situation....they cannot judge because they are not a part of your relationship with your daughter. I totally understand as I got alot of this as well, but I just kept telling myself that I was doing what was best for my son. There is no reason that 12 months is some "magic age" and that suddenly the day they turn a year they don't need breastmilk anymore and the day before when they were 11 months they did. It is just a superficial limitation to childhood that western culture has decided. They grow up fast enough anyway...why push them?
I hope you don't take offense to this or disregard thinking I am a "breastfeeding wacko" or something. But there really is nothing wrong with it. And if you are able to come to terms with it and accept it I think that your family as a whole will probably be a lot less stressed and tense about it.
http://www.kellymom.com/parenting/velcrochild.html
http://www.kellymom.com/bf/bfextended/toddlernursing.html
http://www.kellymom.com/bf/bfextended/ebf-benefits.html
Nursing does not only fill a nutritional need, but also an emotional need. It seems like your daughter still has that need, so trying to take her main source of comfort away at this point *I* think would be counterproductive. But you obviously have to do what is right for you and your family. Good luck with your decision. Weaning is a difficult thing no matter when you do it.