I agree with DVMMOM that you should talk to the administration and teacher and say that these visits by not one but two adults to your children must end.
I do fault the school for allowing visits on the playground, in the cafeteria, in the classroom too--? Our school would never, ever let that go on. Parents can come to the lunchroom, period, unless they are volunteering. You must have a reason to be there. And beyond that, the classroom teachers do NOT want parents there unless the parents are volunteering for a specific need as identified by the teachers! I am amazed and appalled that the teachers have not already spoken to you pretty harshly about grandma and great-grandma. And our school also has a clear policy: Do not bring outside food in for your kids if they already brought or bought a lunch; it is distracting to other students.
Sorry, but when you caved and told your mom you were just kidding about her cutting back her visits, you in essence gave her your permission to continue this mess. Time to stiffen the spine and tell her AND your own grandmother that this is over, starting in the next school year.
Tell them that the school AND YOU believe that having visitors is distracting to other students. Point out that the reason grandma does not see heaps of parents and grandparents visiting during the school day is that those parents and grandparents are respecting the teachers by not coming in and distracting the students. (She will fuss and fume but stick to your guns and say it over and over if you must.)
You also have an excellent chance, with summer now here, to establish some new rules with these women, your own rules. I would bet that once school is out, grandma is going to be all over your family, wanting to take your girls here and there all summer long. Is that a correct assessment? If so -- nip it in the bud this instant. Have your girls booked up, even if that means "We have plans today" and nothing more formal than that. If grandma tends to drop in unannounced: "The girls all have play dates/camps/classes/we're doing a day trip, so please call this summer any time you think you would like to see them and we will see when we can work it out." If you are at home and she comes over unannounced, feel free to say, "Sorry, mom, this is not a good time. How about Wednesday at 3?" And so on. She has gotten away with doing what she wants, when she wants, for too long. Only you can prevent this becoming truly toxic.
I feel horrible for you. Grandma thinks she is being very involved with her grandkids and is a wonderful grandmother when in reality she is manipulating the school and you, too, to get what she wants when she wants it.
One thing eventually will happen for sure: One of the grandkids will tell you, "I wish grandma wouldn't come to school so much. It's kind of embarrassing." The oldest one will be first to say it. Grandma has zero idea of how kids' social worlds operate. She will then probably "dump" the oldest girl from her visiting roster and show favoritism to the younger ones...until they too grow cool to her smothering attention.
Seriously, you have to stop this so that next year the teachers know YOU are the mom. You have to tell her and the school to stop this. If you really must, I believe the school should have a form that lets you say who can drop off or pick up a child; ask if there is also a form for who can come onto the campus to visit a child. You may have to go so far as to list her as not being allowed to visit. Try first to resolve it by telling her to stop and meaning it this time.