A leaked report also alleges Mahboob Hussain tipped off his son about the upcoming sale of a Sandwell Council property
Author James Goudie QC suggested Labour's Mr Hussain committed six council code of conduct breaches.
Mr Hussain, now suspended by Labour, has previously denied any wrongdoing.
He said he could not comment now as the contents of the report were "confidential".
Former economy chief councillor Ian Jones and Mr Hussain stood down from the ruling cabinet after investigations began, but both had their suspensions from the Labour party lifted before elections on 5 May.
Mr Hussain has been suspended afresh, the party confirmed.
The authority commissioned law firm Gowling WLG to investigate alleged irregularities in the sale of the authority's former properties from 2011-2013.
Publication of this report has been delayed after legal action by "one of the parties named", the council said, but documents leaked to the BBC shed light on its findings.
On the parking tickets, Mr Hussain gave evidence denying he sought favourable treatment.
Mr Goudie QC found Mr Hussain requested "in effect" for parking tickets for his wife and an unnamed son to be cancelled.
He said the wife's penalty was cancelled, while his son's was reduced.
This was among three occasions Mr Hussain allegedly broke the Member Code for councillors to help his family, according to the QC.
Gowling WLG investigated alleged irregularities in the sale of the authority's former properties from 2011-2013, including three old public toilet blocks and a former coroner's office in Smethwick.
A parallel police investigation ended in March with no further action.
Mr Goudie said publication of the Gowling report was "strongly in the public interest".
The QC suggested Mr Hussain's breaches of the Member Code included:
Mr Hussain gave evidence he did not know who was buying the toilet blocks because the purchase was through a company name, not the name of his friend.
He said he had not been consulted and had not been aware of the price.
Mr Jones gave evidence saying he did not know the relationship between Mr Hussain and the toilet blocks' buyer. The QC said this meant there was no misconduct issue by Mr Jones.
Mr Jones also said he could not comment now because the report was confidential. He has previously dubbed the investigations a "witch-hunt" and disputed the truth of the allegations.
Mr Hafeez, who was arrested last year, provided no evidence to the council's solicitors despite requests, the QC wrote. He has not yet responded to further questions from the BBC.
Police told him in November 2015 he would face no action.
He said in November his arrest "did not relate to the sale or purchase of any former Sandwell Council properties" and he was "considering taking legal action against a number of individuals and organisations".
A former deputy council leader "interfered" in parking tickets issued to members of his family, a lawyer has found.