Ouch, she was skinny! Glad she's getting more food than her previous owners gave her, good work
Couple of things possible here.
Firstly, how much handling experience do you and your kids have? It's possible that you unconsciously let her get away with disrespectful behaviour because you didn't recognise it or know how to correct it, and now it's become dangerous behaviour. This is a pretty common occurrence with new owners.
Alternatively, she may have only been quiet when you bought her because she was so starved, and on her lovely new diet has become right full of herself! This is also not unexpected with horses that have previously been weakened by their starved state. They grow a whole new personality once they've finally got some energy.
So...I'm going to throw a whole bunch of questions out there!
1) What is she rearing at?
2) How is she doing it? Does it strike you more as a fear response or an aggression response?
3) Does she paw the ground, push into your space, snatch feed, bite or do anything else disrespectful?
4) What does the other "crazy" behaviour entail? Is it more fearful or aggressive in nature, do you think? Is she over-sensitive to sounds, sudden movements? Or is it more that she's territorial/food aggressive toward people and/or other horses?
5) What is she currently being fed (with amounts please
6) Did you get a PPE (pre-purchase veterinary examination)? And if so, did the vet spot the cancer under the tail?
7) If you didn't get a PPE, or if the vet did a poor job (i.e. not spotting the tumour) then it is also possible that she was drugged. How would you describe her behaviour when you went to see her before you bought? What did you do with her (e.g. picked up feet, led, hosed down etc)? What questions did you ask of the owners where the answers may have raised red flags?
Best of luck in answering my interrogation