She WASN’T independent for FAFSA purposes on the day she filed. She’s under 24, not married or supporting a child, a military vet, etc. She is correct that, if she hasn’t lived with either parent in the prior 365 days, and neither parent has provided more aid to her, she is to use the parent with the higher income, which she did. She can ask for an override, but to do that you have to fill out the FAFSA with the information as it is on filing day. If she made a mistake and her mother DID provide aid to her or she DID live with the mother one day more than the father, then that is a correction to FAFSA and she should correct it and use the mother’s information.
It seems this student did everything correctly and honestly, using her father’s info. Sometimes it is just unfair or unlucky how the FAFSA rules work.
OP, I’m pretty sure you would qualify for instate tuition at Wyoming because your mother has been a resident for a while. The main campus is in Laramie but there are satellite campuses around the state (it is all one system) and there are many online courses. If you finish your entire year at your current school and transfer as a senior, you may have to go extra semesters to complete core or major requirements (and the required History of Wyoming class - required by the Wyoming Constitution for every student!). I’m sure it is not your first choice, but may be an option if nothing else works. Or for grad school!
Your discussion with the FA office sounds hopeful, that they want to work with you. Also that you are trying for the RA position and another job. I think you can make it work.