The lawyers of Jack Sargeant have written a strongly-worded letter accusing First Minister Carwyn Jones of causing "considerable distress".
Mr Sargeant's father Carl was found dead in November, four days after being dismissed from the cabinet.
An inquiry into how Mr Jones handled the sacking will be led by Paul Bowen QC, but has not yet begun.
The Welsh Government said it would "not be appropriate to comment" on the letter, sent to Mr Bowen.
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But on the eve of the Welsh Labour conference, Jack Sargeant's lawyers have said the first minister's approach is causing "considerable distress to our client and his family".
They added: "The inescapable fact here is that someone sadly has lost their life, a much loved family member, and due process must be followed expeditiously to enable to those closest to him to find some closure."
Carl Sargeant was dismissed from the cabinet after being subjected to a Labour Party inquiry into allegations of "unwanted attention, inappropriate touching or groping" when he died.
Mr Bowen was appointed in January to lead the independent inquiry into Mr Jones' handling of the Mr Sargeant's sacking but it has yet to start.
Earlier this year Mr Sargeant's son Jack was elected to represent his vacant seat of Alyn and Deeside in the assembly.
The letter comes at the end of a week where the Conservatives failed in a bid to publish a separate report into whether Mr Sargeant's sacking was leaked in the days before a cabinet reshuffle.
It found no "unauthorised" leaking of information on his sacking but its full details were withheld over fears about the confidentiality of witnesses.
Mr Jones threatened legal action against the assembly over the attempts to publish the report.
He was also cleared of any wrongdoing over allegations he misled the assembly over claims of a bullying culture within the Welsh Government.
Welsh Conservative leader Andrew RT Davies said the first minister's judgement had "come under considerable scrutiny in recent days" and that the lawyers' letter would "only add to the growing pressure his leadership is under".
Mr Davies warned Mr Jones against kicking Mr Bowen's inquiry "deep into the long grass".
Analysis by Nick Servini, BBC Wales political editor
The significance of this letter is all wrapped up in the timing.
The shadow caused by the death of Carl Sargeant was always going to be in the background of what promises to be a packed Welsh Labour conference but this ensures it remains front and central.
From the perspective of the family, there is clearly intense frustration that the main inquiry into the circumstances surrounding his sacking has not even started.
There is difficulty for the Welsh Government too.
Even if ministers share that frustration, no-one can be seen to be meddling in such a highly sensitive area.
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