Agree with everyone else. Try to renegotiate the merit with the acceptances you have. If you haven’t done this yet you will be surprised how many LACs especially will do this. It might not be a ton but perhaps enough to make a difference. Your timing is great right before May 1. Have your daughter write a very thoughtful email to the Admissions Counselor why she liked the school so much, any awards/updates since she applied, perhaps mention that her mother is caring for an ill grandparent and isn’t able to work and that is creating an extra hardship especially since her parents already supported older sibs through college, then list all the comparable schools she’s been accepted to that have higher merit then what she’s been offered. I am not really sure if you should mention the Gap year quite yet?? We went through this last year and I really couldn’t believe that the process was like this but it is!
Then emphasize to your daughter to work and save $$$ during her gap year for college. I can’t imagine any kid would want to go through the entire process of reapplying to college as you have outlined. I think you risk having a very resentful and unhappy kid if you insist on this. Good luck and let us know how it works out!