No, you are not wrong to think that this is the way it has to be. I am sitting here in my TV room while my college freshman daughter is contentedly reading for pleasure on the other sofa. Despite the fact that her dorm room is rather crowded, the academic pace is intense, and she goes to school halfway around the world away from us, she is happy at her school and is starting to look forward to heading back there and being with her new friends again as we enter the third and last week of her break. I think this is how it should be for most high functioning college kids.
It seems like you have tried to help your daughter work through her struggles with the first term, however, the solutions have not given her (or you) the desired results. It is hard to grapple with giving up such an amazing educational opportunity that your daughter worked hard for, but it is also hard to watch your daughter struggle so much and risk more serious mental health consequences as her stress goes unresolved. It seems like you are at this point now of deciding to fish or cut bait so to speak.
It sounds like transferring might be a good option, but can’t really advise you as to whether or not leaving before the sping quarter would be best or not, or what the financial ramifications would be. It seems like you have lots of phone calling in store to ask these questions of the advisors at the schools, and a little time to get it figured out before the end of the current quarter.
My heart goes out to you. Tears and pain in your child are not easy. It will be good for your daughter to see that she isn’t stuck and that problems can be solved.