A couple of thoughts:
1) Ask great-grandma herself if that is her preference - my DD's great-g'ma loves every opportunity to see her, yours may too!
2) Also, really evaluate your daughter's ability to behave at that (or any other) restaurant. Can she/will she eat the food, stay in her seat, and be quietly entertained for the majority of the dinner? Is it really kind to her to bring her if she can't?
3) If you don't bring her, I agree with the other poster, your daughter does not know or care at the age of 2 that her birthday be celebrated on her actual birth date. Have a big special birthday breakfast that day and then celebrate with a party or whatever on another day, and she'll enjoy it just as much. [My oldest DD was born on Dec 30th and we have a very little family celebration (just us and the kids and a cake) on her actual birth date. We do big parties for her every year, but never so far on her actual birthday - it is too close to Xmas and New Years and we travel out of state for Xmas every year. She's only just turned 4, so that may change as she gets older (and the parties get smaller), but right now, she's so excited about the parties, she really doesn't care what day they are on. And the bonus (for her) is she gets multiple cakes/parties. = ]
3) Great-Grandma, however, is very aware of when her birthday is and the fact that it falls on a Saturday this year may make it important to her to celebrate on the actual date. #75 is also a pretty big milestone, she may not have a big party every year. As a member of her extended family, you should probably go, and they may not have very many shared birthdays left, after all.
4) If you do care so little for Great-Grandma, since she is not 'technically' related to you (although she is, the legal marriage of you to her descendant does makes you technically related, if not by blood), then don't attend *and* don't make waves. Your husband should attend and just let the rest of the family know that you couldn't get a sitter, so you stayed home so that he *could* join the party. No need to mention the DD's birthday. Win-win situation and shouldn't get your in-laws in a snit.
Good luck!
PS - If you haven't done so already, a nice keepsake for each of the birthday girls would be a picture of just the two of them every year on their shared birthday. = )
***Response to your 'on another note" - definitely choose to stay home and enjoy the evening with your little girl. Give your DH the option of going if he'd like, and don't hold it against him if he goes, but I'm with Megan, if you go, you'll just stew over it the entire time and not enjoy yourself. Better to claim lack of a sitter and let him attend to represent you both to the family to keep them happy. I'm often on the 'outs' with my in-laws as well, so I think that trying to keep the peace is worth it (to you) in the long run.