A government overhaul of the childcare system has left some of Australia’s most vulnerable families without access to care, with the agency responsible now telling parents to find their own support workers.

In one case, a newborn baby was unable to be discharged from a hospital in Sydney for four months because the family could not find an in-home care worker.

Changes to the childcare sector have reduced the subsidy for in-home care, which some providers say forced them to stop offering the service.

Families accessing in-home care often include children with disabilities who need additional care to that provided by the national disability insurance scheme (NDIS), parents suffering physical or mental health issues, and those referred to providers by child protection services or other agencies.

Dozens of families across Australia have lost their in-home care or are now required to pay a gap fee where the support they had been receiving was previously fully covered.

A social worker at a paediatric hospital in Sydney, who spoke on the condition of anonymity, told Guardian Australia that since the changes came into effect in July she had been unable to place children into in-home care.

She cited one case of a newborn boy whose mother needed a carer because he had to be fed using a complex system similar to a drip called total parenteral nutrition.

“He could have been home four months ago,” the social worker said. “Every night in hospital costs $1,000.”

The social worker said she had seen two cases of children with autism where the only respite for the mothers was when the children became sick.

“With a bit of luck they keep going and then the child gets sick and comes into hospital and they have a bit of a break with the nurses doing the feeding and stuff like that.”

Jessica Ezra, from Bondi, a mother of two children aged three and 12 months, said she lost access to her carer and was facing difficulty to obtain a new one.

In response to growing complaints about the changes the education minister, Dan Tehan, on Friday announced the government would inject $44.5m in funding to boost the subsidies and increase the number of places by 200.

“The new rate cap balances the needs of families to access affordable education and care with the interests of providers,” Tehan said.

Ezra’s oldest child, Elisha, has kidney reflux, a developmental delay and Prader-Willi syndrome, a chronic condition that means he is always hungry.

She had previously been assisted by a carer who worked in the home between 8am and 6pm, helping Elisha with his development.

“He needs an aide, one-on-one, all the time,” she said. “I can’t leave him by himself, I can’t leave him around food.

“It’s been really difficult … I don’t have family here and neither does my husband.”

As part of the changes, the government enlisted an in-home care provider, NSW Family Day Care Association, to act as an agency to determine parents’ eligibility and organise care for families.

Having contacted the agency in August, Ezra, who has since turned to a fundraising campaign, said she was told by the agency there were no carers available and she would be placed on a waiting list.

She was also told her application could be fast-tracked if she found her own employee, who could then be employed by the agency.

“Now I’ve had to go public with my son’s condition, which I never wanted to do because I didn’t think it would help him,” she said.

The NSW Family Day Care Association was approached for comment.

Sophie McGinley, the managing director of Balance Home Services in Adelaide, told Guardian Australia her business had previously provided in-home care to 35 vulnerable families, including mothers with postnatal depression who could not look after their baby while heavily medicated.

“They were referred to us by the department of child protection or Helen Mayo house that deals with very high level depression,” she said.

McGinley said the families she had provided in-home care to were no longer receiving in-home care.

“The subsidy that the government pays now would leave them with an out-of-pocket expense of $20 an hour, which they just can’t afford,” she said. “Often these people are in these situations where they are unable to work.”

The Greens education spokeswoman, Mehreen Faruqi, urged the government to “step in and fix this problem before these vulnerable families are pushed to the brink”.

“These stories are heartbreaking,” she said. “Families and children in need are suffering because the government didn’t think through their decisions.”