I am a buddhist, have been for twenty years, but I was raised Episcopalian and my family is seriously religious.
You have to understand one thing. Baptism is probably THE most important thing to a grandparent, and what happens after that is not so important. Here is why. If a child, at least in the Episcopalian church, dies without being baptized, they do not go to heaven. So for a serious believer like your grandma, it is probably MORE important than anything that your kids be bapitized. I do think that if you do that, the rest of the picture will be must less "charged."
My mom, who never asks for anything, kept bringing up our baptizing our two daughters in the Episcopalian church. I know for her it is a fear that they will die and not be able to go to heaven. ANd this is a real fear, on her part. Her fourth child died at two and half (can we say traumatic?) and so of course, new life is overshadowed with the possibility that there might be death. A huge comfort to her was / is that her daughter Carolyn is in heaven.
SO, intuiting this (she never said all this as the reason for her asking for them to be baptized) ... I agreed to baptize both girls last summer. For her. But also for them. We are raising them buddhists, but I want them to have real exposure and teachings in other religions, even ones with flaws. I really, really disagree w/the notion of god, heaven, etc. but this is not about that. It's about setting my mom's heart at ease and also letting my kids see there are other religious paths.
If i were you, I'd baptize your child for her sake. She's been so kind to her. It is strange to say the words you don't believe, but there are larger truths happening there in the ceremony ... the love of the family, the rejoicing over new life, the support of the community ... focus on that.
I was lucky, I could discuss w/the priest that I didn't believe all that I was saying during the ceremony, he said fine, you just have to say it .... we all have doubts/don't believe, etc.