I'm sorry to hear your daughter has had cancer. It must have been really tough for you and your family. I think describing a two year old or even a four year old as a chemo brat is really unfair. My son is nearly four and he never sits still and thankfully he has never had a serious illness.
We are in England and Andrew is under a child development centre because of developmental problems. The child development centre is lovely because you can see several health proffessionals at once, reducing the number of appointments. I think your little girl would benefit from seeing a community paediatrian for a development review where they dont focus on the fact that she has had cancer.
Andrew walks on tiptoes and has delayed speech. We had some behavioural issues and our paediatrian arranged a hearing test and speech assessment. It turned out that andrew had glue ear which caused him to be frustrated and led to bad behaviour.
Maybe your little girl has a medical problem like glue ear which has nothing to do with the cancer.
Sorry to hear about your daughter.
The way i see it is that she has had a rather difficult childhood- She is still not fully well though that may not justify her behaviour in your eyes yet her experience of childhood has been one of greater pain as compared to that of other children. Maybe if you tried a completely different approach of encouraging the good things that she does, praising her for when ever she behaves well, treating her to good times and happy experiences & things that she likes whenever she behaves relatively better and always demonstrating your love for her irrespective of the way she is or the difficulties that she may be causing.