A government program that forces parents to take their children to activities such as playgroup or swimming lessons to keep their parenting payments is to be examined by a Senate inquiry.

Guardian Australia revealed last month that parents, predominantly single mothers, were being told to undertake activities including “story time” or to begin study at their own expense under the $350m pre-employment program ParentsNext, which was rolled out nationally this year.

On Tuesday the Senate voted to conduct a wide-ranging review of the program, including its aims, whether it should be compulsory and whether participants should be subject to the same penalties that are imposed on other welfare recipients.

The Greens senator Rachel Siewert said the inquiry, which has been co-sponsored by the Greens and Labor, would allow the upper house to understand whether the program was the “best way to help parents”.

The committee would hear from “single parents affected, most of whom are women who, rather than being supported to raise their children, are subjected to a mandatory program that is resulting in adverse outcomes”, she said.

News of the inquiry comes as more participants speak out about the program’s impact on their lives, and as mothers campaign for it to be made voluntary.

Margaret, a Riverina mother who did not want her surname used, is a domestic violence survivor who said she had been re-traumatised in the process of seeking an exemption from the program.

She was eventually granted a 12-week exemption from completing any required activities, but said she had been forced to retell her experience to the outsourced ParentsNext provider, despite having done so days earlier at a Centrelink office.

Margaret’s request to do the interview over the phone owing to safety concerns was denied. The mother of three said she had no one to care for her youngest daughter, four, who had to come along to the appointment.

“Four-year-olds are not stupid,” she said. “She was sitting two metres from me, playing with blocks. And of course when I had to start explaining my situation, they were asking about the domestic violence and whether my daughter had seen the domestic violence. That’s none of their business.

“I was in tears and then I’ve got my daughter coming up and hugging me because I’m crying again. ‘Because Mum does cry a lot, because Mum is sick of telling the story to everyone.’”

Margaret still needs to report her income, something she did not have to do before she was pulled into the ParentsNext program. Failing to do so will mean her payments will be suspended.

The impact on mothers like Margaret will also be examined by the inquiry, which will consider the “measures, if any in place to avoid causing risk or harm to vulnerable participants and their children, including participants and children who are victims and/or survivors of family violence”.

Under the current guidelines, the government hands the power to grant exemptions for reasons such as family violence to ParentsNext providers, rather than the Department of Human Services.

The chief executive of the National Council for Single Mothers, Terese Edwards, said family violence exemptions should be handled by the department, not private providers.

“The department has had years of training, including there was a law review commission review into how government departments handle domestic violence … The other reason, that they can then work out whether there are other supports could be helpful, whether a mutual obligation exemption is required or whether they could qualify for a crisis payment.”

For survivors, Edwards said, talking about their experiences of family violence “because you have to is re-traumatising”.