The first question to ask is there a partnership agreement? A well drafted partnership agreement would address issues such as what happens upon the death of a partner, valuation of the business at the time, whether the partnership dissolves or not etc. You need to establish if the personal reps of your Dad's estate steps into the shoes of your Dad in the partnership.
If there is no partnership agreement, then the provisions of the 1890 Partnership Act kick in.
You should establish if the partnership had an independent accountant. Such an accountant would have a duty of care towards your Dad. In this case it does seem that there are independent accountants involved. The pragmatic way forward is for your mother to send a copy of the grant of probate to the remaining partners and ask them to authorise the accountants to release the required information.
If the partners are unwilling to pay the monies due to the estate then, subject to the terms of any partnership agreement, your mother could apply to the High Court to have the partnership dissolved and the assets distributed.
Hopefully the other partners will not try and take advantage of the situation.
Jim Stafford