I'm at a loss...

As most of you know, I breastfeed Brentley. I tried breastfeeding Grace and failed miserably. I barely made it to her being 2 months old before I gave up (which is one of the biggest regrets I have). So, she hasn't breastfed in quite a while now. However, just recently, she has taken interest in it. She will come up to me and tell me she wants to eat, then she will try to lift my shirt up. At first I figured she was just being silly, then she did it a few more times, and it is to the point now that when I tell her she can't she gets sad. I can tell it hurts her feelings that she's not allowed to, but Brentley is. I figured it was just a phase that she would get through, but it doesn't look like that is going to happen anytime soon :( I try to explain to her that it's for babies, and that she is a big girl, but she just doesn't understand.
And there is a whole other part of me that almost wants to let her do it just because I feel that I failed her when she was a baby, and this would almost be making up for it. Now, I'm not going to. It just feels weird. I have nothing against people who practice extended breastfeeding. I am one of the people who believe that different things work for different people. And in my case, I do not feel that allowing her to breastfeed would be a good thing. It just brings up a whole host of emotions. Now, not only have I failed at breastfeeding her, but I am denying her when she wants to breastfeed, and she thinks that I am being mean. I just feel terrible. In all reality, she more than likely wouldn't even be able to get anything out because she wouldn't be able to latch properly now (especially since she didn't even latch properly as a baby). But I still feel terrible. I can't figure out how to explain to her that I'm not trying to be mean.
I tried posting this on Cafemom, and most of the replies I got said that I should let her try it. Some said that I should let her try it just to get her curiosity out, and others said that I should let her try it to see if she would take to breastfeeding...
I don't want her to take... I already have anxiety about weaning Brentley. I can't imagine having to wean Grace as well.
Others were saying that I should just pump and let her have it that way. That is not what Grace is wanting though. Heck, I have a whole freezer full of breastmilk (about 200 ounces) that is pretty much just going to waste. I could give her some of that if that is what she wanted (and yes, I tried giving some to her in a cup). She wants it from me. I can tell she wants the experience, not the milk. Which makes it that much more difficult to tell her no.
Gah, this is just so stressful. It makes me feel like a bad mom.

I know, I know, this all sounds really weird. Most of you probably think I'm crazy that I even consider letting her do it. You would just have to be in my shoes to understand why. And I'm not going to let her, but I've got to figure out some way to stop breaking her little heart every time...