Please receive my condolences. I am a bit unclear about where you are but from the question I understand this happened in the UK. The succession law is not unique in the UK, but is different for England and Wales, Scotland, Northern Ireland, and the other territories, each having separate laws for such matters. I will presume we are dealing with English law.
The basic principle is that a person who is a joint account holder may have access to the account at any time, and, from the bank's point of view, does not have to justify it. Justification happens, on a private level, between the two co-holders of the account. Therefore, the money taken from the bank account before the time of death are not per se illegal, as she was entitled to take it. The question is what did she do with them, and, if they actually belonged to your mother, whether she can justify using them according to her wishes.
Furthermore, she should not have distributed the money in the account without a probate.
The way to contest her decisions is to ask for her removal, and potentially for a court-ordered inventory of your mother's assets, asking it to include the money she took before, so that it is included in the money to be distributed.
Please look at these two informative pages (not meaning to promote them, just they are quite clear about what can be done): here, and here. The relevant legalese (the Civil Procedure Rules for filing and dealing with such claims) is here.
I hope my answer was useful and that you will have success in your endeavor.
Dr I L Vlad