Ray, I think you've probably missed the boat. if there was no formal arrangement, you are not going to get 3 years accounts - it will be impossible to say what purchases your mum made, what purchases your brother made on her behalf and what purchases (if any) your brother made on his own behalf. the time to have asked for accounts to be kept would have been 3 years ago. Aslo, what seems unreasonable to you may have been perfectly reasonable between your mum and brother.
I was in your brothers situation with my mother in law. She has 5 geographically widespread children and we got her into sheltered accom near us. She asked us to help out with her finances but there was never a POA in place. We made withdrawals on her behalf, paid bills from her account on her behalf and as she was asking us to do it, we never made notes. She gave us her PIN and internet banking details to do this. I could [robably look back at her bank account and see what was for what, but she used to like having cash in the flat too, so would ask us to withdraw, say, £400. I couldn't prove that I just didn't take the £400 (I didn't)
As I said, if there is no will, someone will need to apply for letters of administration (if her estate is likely to be over £5k). If she has no husband, that could be either you or your brother. I will warn you though, sorting out someone's tricky estate isn't a job for the fainthearted!