I'm not sure I can give advice on managing uncooperative people, that's something that has to be decided with full knowledge of the people and the circumstances. But I'll try to comment on some relevant considerations.
There are a number of levels of checking that should be followed by a local council. The financial standing orders should define them, and councils are expected to review their financial standing orders annually. The first level of checking is that there should be councillors appointed as councillor auditors to check that financial transactions are being recorded accurately and are based on lawful council decisions. The council is required to make declarations as part of the creation of the annual return to say that proper controls have been in place. If you haven't got one to hand, it is worth getting hold of the last annual return to look at precisely what is involved.
The next level is the internal auditor. Despite the name, the internal auditor must be independent of the council. I'm puzzled by the internal auditor having resigned at the end of the last financial year, unless that is a rough description. The internal auditor can only check the records for the year after the end of the financial year, and the external audit relies heavily on the report from the internal auditor (which is an important part of the annual return). So, perhaps the internal audit was completed for the last financial year prior to the auditor relinquishing their responsibilities. An internal auditor must be appointed in good time for the work to be done within the timetable laid down for the annual return production and external audit.
The final level is the external audit. This is a very skimpy audit by most standards, and relies on checking that large movements have been explained and that there is a satisfactory report from the internal auditor. But anyone dissatisfied with the council's record keeping or procedures is entitled to provide information to the external auditor and ask for them to take action. It is less likely that the Monitoring Officer will take an interest in financial matters.
Councils should always comply with their own financial standing orders, and it is good practice to provide regular financial summaries to the full council. Beyond that, councillors have a common law entitlement to have access to most council information on the basis that they cannot properly carry out their functions without it. This certainly applies to financial records, so councillors are entitled to ask to inspect them, although they should be reasonable as to the practical details.
Which course of action will be most fruitful depends on judgement, as implied in your last paragraph.