Katie Allan, a student at the University of Glasgow, took her own life in June 2018 at Polmont while serving a 16-month sentence for a hit-and-run crash.
She had a history of self-harming and had previously been preferred to a community mental health team by her GP.
Four months later in October 2018, William Lindsay took his own life while he was on remand at the young offenders institution near Falkirk.
Mr Lindsay, who had been in care repeatedly, died three days after being admitted as there was no space in a children’s secure unit – despite him having a history of making attempts on his life.
Their suicides followed a series of deaths in Scotland’s prisons, which prompted a Scottish government review into how deaths in jail are handled.
The Crown Office and Procurator Fiscal Service (COPFS) said Katie and William both died while in legal custody at Polmont.
In 2022, the Crown Office told the families there was enough evidence to prosecute over their suicides but the Scottish Prison Service is immune from prosecution.
Katie’s parents are both expected to give evidence at the start of the inquiry.
Speaking on behalf of Linda and Stuart Allan, Mr Anwar said: “They feel they have been failed by the Scottish criminal justice system since the day of their daughter’s death.
“Yet today they are once again facing another process that cannot apportion blame.
“Katie’s parents believe that the Scottish Prison Service has no accountability for the avoidable deaths of young people.”