This day is about your daughter. It's wonderful that you would even consider inviting someone that toxic to the party just to make your husband's grandmother happy, but it would clearly cause you stress, and as we all know, our kids feed off of our stress. Your daughter deserves to be "Princess for a Day", and that will be hard for her to do if mom is under fire.
As you said, GMIL wants to get everyone together on EVERY occasion. She must surely know that it isn't possible EVERY time. And while you have invited some family, you have also invited friends, which means that this does not qualify as a "family function", and your friends probably would be terribly uncomfortable to be exposed to any family drama. If necessary, just gently explain to her that while you understand and respect her desire to have her brood all together as often as possible, you feel that it is not in your daughter's best interest for the SIL to be there. She might be a little disappointed, but will probably be a minor disappointment, and your description of her leads me to feel confident in saying that she will understand.