Can you find a school where you pick majors later? If you are saying you are a non-engineer they may care less about Chem. Does she have evidence of other interests?
We visited URI and UVM and pretty sure neither requires direct-admit to engineering and that you can switch in. (For URI you technically don’t enter a major right away until done with some core class - brand new engineering building too!). This is dicey, overall, but the chem thing is hard. They are very different than UTK though.