What did your DD get for GCSE Physics, Teen?
DS is finding the Physics more difficult than the maths, and TBH, I was exactly the same 35 years ago. I'm still not exactly sure how I passed! Not everyone finds FM the most difficult.
The Physics teacher at DS's old school told me that A level Physics is 50% maths. (Which of course means that 50% of it isn't maths...!)
If your DD got a 7 for maths, then she scored somewhere between 60% and 70% in the exam, meaning that she couldn't do 30% of the exam. If the 30% was the more algebra type stuff, then that would explain why she is struggling now.
On the other hand, she did pass that test for doing FM... so either your DD is up to it or the college's screening processes are not very good. You could probably work out which it is by looking at the college's FM A level results for the last couple of years!
I get what you are saying about your DD not doing enough work, and that won't be helping things, but maybe she's been given bad advice too?
Is it too late to change course? If it is, then your DD needs help now. I understand that she doesn't want you involved, and there will be hell to pay if you do something against her express wishes, but I think in your shoes, I'd contact college anyway and ask for a meeting for the three of you to work out how to get your DD back in track.
The threats about not working unless you do exactly what she says are empty. It doesn't work that way i.e. students work even if the conditions around them aren't absolutely ideal. No one lives in a world that is perfect. The only person she'll hurt by not working is herself, and that's her choice. Given that she's already chosen not to work in the past, there's a reasonable chance she won't in the future either, but it's her choice what she does and she'll be the one who will suffer if she doesn't. Whether she works or not isn't conditional on whether you obey her or not, no matter what she says.