Is the mother also a member of the Council? When they allege wrongdoing, the Chair should ask them to clarify which rules have been broken, by reference to the standing orders and financial regulations, or other policies. If they can't be specific, ignore it and move on. If they're moaning about issues not relevant to the meeting, they should be addressed afterwards.
FOI legislation is not the catch-all people expect it to be. The Council has a right not to respond to FOI requests that are considered frivolous or where the information is available from another source, so each request should be considered on its merits. I would be interested to hear what has been requested under FOI, as Councillors should not be using these provisions. I have declined to respond to more than half of all FOI requests I have received and on the one occasion when I was reported to the Information Commissioner's office, they agreed with me.
The disclosure of confidential information is a serious offence and could land the Council in hot water, so if you have sufficient evidence, this should be submitted as a code of conduct complaint. The Monitoring Officer shouldn't ignore such a complaint against a district councillor, even though it doesn't relate to that role.
Who decided that the previous Clerk should receive a very large payoff? Was this negotiated through the Council's insurer?
Finally, the section of the model standing orders regarding disorderly conduct at meetings applies to both councillors and members of the public. If members of the Council behave in a disorderly manner, the Chair may invoke these powers. Used in a calm and professional manner, they are a useful tool.