The transport minister has been under fire after it emerged a department employee - dubbed a "political operative" by the opposition - was involved in political work while working in her office.
She denies knowledge of Mr Ash's conduct until recently, a position Premier Chris Minns has accepted.
Ms Haylen has referred the matter to her department for investigation.
One of the MPs who will interrogate the minister in a budget estimates hearing on Tuesday says the government is trying to sweep the matter under the rug.
"They are seeking to sweep this aside, burying it on Melbourne Cup Day, withholding documents and hoping this will all go away," coalition transport spokeswoman Natalie Ward said on Monday.
"Well, it's not going anywhere. We've got a lot more to ask about it."
The Melbourne Cup Day hearing comes after Ms Haylen also faced repeated questions in parliament over her appointment of former Labor government staffer and infrastructure executive Josh Murray to lead the transport department.
Ms Haylen has defended Mr Murray as the best person for the job.
The premier went into bat for his transport minister on Monday, dismissing concerns she may have breached the ministerial code of conduct.
"A reasonable person would expect Jo Haylen to focus on the job of running the transport department which most people believe needs a lot of work," Mr Minns said on Monday.
"She's the right person for the job."
Also facing budget estimates will be another minister under fire on several occasions since Labor's election win in March.
Police Minister Yasmin Catley has faced criticism for her handling of the police tasering of dementia patient Clare Nowland and officers' counselling of the Jewish community when the Opera House was lit in Israeli colours.
She will face questions alongside senior police led by Police Commissioner Karen Webb.
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