M.B.
I nursed both of my boys well beyond two. By that time, they were only nursing once or twice a day. If you let them wean on their own terms, then life is easy and you'll be able to continue to meet her emotional needs. There is a wonderful book entitled "Mothering your Nursing Toddler" and that really helped me understand how natural and important nursing your toddler can be.
That all said, you do have a right to assert some of your needs into this process. Your daughter is reaching the point (and may already be there since breastfed babies IQs are typically higher :) where you can negotiate considering both your needs. This is also a very important step in your daughter's development and developing this skill now will go a long way in parenting your daughter later (especially during the teen years).
When my sons reached that age, they were aware that we no longer nursed in public, but that we could nurse at home before naps or when they were in a crisis situation (injuries, just a bad day, etc.). In my experience we mothers have no better tool than nursing to comfort our children in these situations. I personally believe it's important at this stage because they cannot verbally communicate any of their emotional needs. Also, almost 16 years after starting this process with my boys (which lasted almost 6 years!), this is the one decision as a parent that I have zero doubt was absolutely right.
Also, around two both my boys seemed to not need the nursing at bedtime since we started reading at bedtime. We had been reading since they were about 9 months, but usually before nursing. However, it reached the point where my younger son was not nursing to sleep, so we just started reading at bedtime. After that point, he would just nurse first thing in the morning. As, we had also reached the point where nursing wasn't needed at naptime.
Since you are trying to cut her off, her being more obstinate means that she has a very strong need for the nursing relationship to continue - this is the most intimate relationship you'll ever have with your daughter and continuing nursing sends the message that you are there to meet all her needs.
I do understand your situation since you are a single mother per your profile, so you don't get many breaks. What might help you deal with this better is to ensure you have some "me" time - don't feel guilty about this and get friends to take care of her on occasion. Or, leave her with her regular childcare provider and take some time off work (if you do work).
My boys are now teens and they are very independent yet they know I'm always there for them. My younger son nursed longer and he is just much more of a cuddly child and he needs lots of hugging and physical contact. Some folks are just like that. Based on my experiences of not being nursed and coming from a large family and growing up very insecure and constantly wanting more attention from my parents, I can see a huge difference in the self esteem that both my boys have. I also personally believe it helps them have a much more natural understanding of women and a respect for breasts as something for nurturing rather than sex objects...I obviously could go on and on about this topic, but I just wanted to share that I have seen long term the positive effects of allowing a child to wean at their own pace. Biologically and based on anthropological research by a Phd at Texas A&M, the natural weaning timeframe for humans is actually 4-5 years!
And, finally, I learned when my boys were 7 and 10 that they had celiac disease and were allergic to dairy. In hindsight, I believe this gave them an additional reason for extended nursing. They were not getting all their nutrients from food (due to the gut damage) thus the breastmilk, being the perfect food and most digestible, likely was still meeting nutritional needs beyond 1 year. In addition, since they likely didn't feel physically well (again something toddlers can't communicate and even so, to my boys, how they felt was normal, although they had frequent tummy aches).
Finally, I just want to applaud you for nursing so long and considering your daughter's needs. You are both far healthier for the experience (the longer you BF, the lower your risk for breast cancer). That all said, you do have to listen to your own instincts as to what's best for you and your daughter. But, just beware that you are not at all alone in nursing your toddler. You might want to contact a local La Leche League support group - www.llli.org - those ladies were wonderful role models for me in terms of extended nursing and learning how to set appropriate limits and still meet your child's needs.
One addition after seeing other responses - children this age are not really capable of making a conscious decision to manipulate or blackmail their parents. If this seems to be the case, they are just using the only tools that they have to get their needs met. What they perceive as needs might not be so obvious at first, but if you sit back as a parent and try to consider the basic needs of a child that age - food and comfort/emotional attachment from their parents, along with the ability to start exploring their world, you can often figure it out.
IMHO, the only times we should be using our "executive" authority is in keeping them safe and setting limits in terms of how they interact with the world (i.e., eating cat food, pulling the cat's tail, writing on walls, etc.). Trying to restrict childrens access to food or comfort/emotional attachment just doesn't make sense (ever in my opinion). The parent-child relationship is the most important one you'll ever have and not considering the child's needs in these sorts of interactions is a recipe for disaster. This is just so very different than debating about curfews, whether it's appropriate to pull the cat's tail, whether a particular video game or movie is appropriate, whether it's okay to climb up the banister, etc. - all those cases are where it's entirely appropriate to assert your authority as a parent. And, in my experience, this is one of the toughest thing to learn as a parent - it really is the difference between a "need" versus a "want" and as parents (and as a society as a whole), there is a huge price to be paid in later years of not meeting our children's basic needs in the early years.