Ok here's here's my two pennorth. I think I see both sides of the argument for and against hunting, but I have no sympathy for this person. The Cottesmore did the right thing by getting rid of her asap as the legal sport of hunting currently has a bad reputation in the public eye.
However,
1. How come the incident was filmed by the Sabs? Balance of probabilités leads me to think they were aware that something similar might just happen because it's happened before. Well done them for being in the right place at the right time.
2. The RSPCA might have been awaiting evidence to allow them to deter others from simply thinking they could get away with mistreatment. Presumably the police rejected taking any action.
3. A criminal conviction has to be declared in job applications, would you want her to be able to work with animals/children / vulnerable adults? Without a formal record she could do.
4. Her actions brought her own professional behavioural standards (teaching) into question as well as sullying the school's reputation. Hence after investigation she was dismissed, but may still be a "qualified teacher" due to no criminal record.
If somebody cannot control their frustrations then they have no place being in a position of a trust.