You need to stop all exercise with your dd right now as she’s been losing weight for quite a while. If she’s not hungry after playing an energetic football match, she’s in big trouble and basically eating through her muscles. It’s likely that she’s not year showing signs of being physically unwell because of the amount of muscle she has built up over the years.
My dd was the same, until she was not. At some stage, my dd suddenly lost all energy and needed to be on bed rest to keep her out of hospital. She was very mentally and physically unwell.
The exercise your dd is doing will not just be shredding her muscle but also depleting her bones. The heart is also a muscle and depending on where she is, it can be very dangerous to raise the heart rate when emaciated. If the heart is compromised and electrolytes not in balance (which you won’t know without blood tests and an ecg), it takes longer for the heart to recover. If it needs to beat within the recovery period, the heart fails. Ie stops.
As your dd wasn’t slender to begin with, don’t be fobbed off by the fact that she may be the same size as any naturally small framed, very slim girls her age. You can be severely unwell with a body weight in the normal range. My dd at 16 never got down the weight that I was at 16 and I am taller than her because we have a very different muscular skeletal structure. And she was very physically unwell when I was not.
It sounds as if your dd needs an urgent referral to CAMHS. Going to the GP is absolutely non negotiable and if you need 2 of you to take her, that’s the priority, not work.
As for her brother and her dad, they need to bloody stop right now. Your ds needs to be told the punishment will be something quite severe each time he says bad things to her. And explain why. She is seriously unwell and if he cannot contain himself then he doesn’t get to do x beloved activity or have y thing. And your dh needs to know the impact of his words.
As for you, I can understand your health risks and I would suggest doing what you can so that your dd sees you eating a decent quantity of food.