OP also has a misunderstanding about who exactly attends Ivies. There are plenty of students with parents whose backgrounds are questionable - but it was the students, not their parents, who applied to attend those schools. If you were such a student, would you make your parents’ background known? I think not! You would do everything in your power to distance yourself from that background. So she may in fact know such people, and not even realize she does.
This sounds like an overbearing parent who is way too involved in her daughter’s application process. She wants her daughter to attend a school with a strong STEM program, and dismisses the Ivies as being weak, yet won’t allow her daughter to apply to top STEM schools because she doesn’t have perfect scores? She dismisses other top schools because of possible cultural contamination from liberals who spend time at the beach. She has her daughter apply through Questbridge, and is upset that at least one school attempted to get more financial information. It almost makes me wonder of she conspired with Dad to remove him from the picture so she would be eligible for that “zero” EFC.
I hope the OP’s daughter attends school away from her mother, and gets out from under her thumb. Maybe she can go to Colorado and become a ski-bum.