Mr Ross said women had suffered “disproportionately” by the economic impact of the Covid pandemic.
His new after-school policy, for children in primaries one to three, would “give opportunity to thousands of Scottish women with the promise that they do not have to give up on their job to look after their child”.
In a speech to launch his party's Holyrood election campaign on Monday, Mr Ross also said violence against women and girls was a “vile blight that is still too prevalent in our society” and while the murder of Sarah Everard had “shocked us all”, it was not an “isolated incident”.
As a result, Mr Ross said, his party would "do everything in our power to combat it”.
He also attacked the SNP for failing to support women and accused them of “covering up” evidence on how the government had handled sexual harassment allegations against Alex Salmond.
Mr Ross raised the 2017 case of former SNP MSP Mark McDonald, who stood down as a minister before quitting the party, saying he had “harassed women” and pointed to the latest claim that has seen MP Patrick Grady “accused of sexual harassment”.
“It is time for the broken Scottish National Party to pay the price for failing women and covering up allegations,” he said, and “for sending the wrong signal – again and again – to women, and to any victim, who challenge powerful people”.
Mr Ross also said the Scottish Conservatives would repeal the just-passed Hate Crime Bill if they won the election – legislation that has drawn much criticism for its lack of protection for women – and would also introduce Suzanne’s Law, which would deny parole to murderers if they failed to reveal where their victim’s remains were hidden.
However, when asked if his pitch to female voters was a recognition his party had a problem in attracting them in the past, he avoided the question.
“Women make up 51 per cent of the population and it’s important for all parties to address policies for women, for men, for adults and young people,” he said. “Hopefully through the policies we’ve been developing people can see that they hit home to people.
“Women have been let down during this pandemic. They are more likely to suffer in a recession, in the difficult economic situation the country will find itself in, so let’s be up-front. Let’s offer the policies which will help them stay in work and get proper support over the next few years, which are going to be very difficult.”
His new childcare plan, which offers just one hour of after-school care per day, would cost £10m for initial pilot schemes, rising to £160m per annum if there was full take-up, paid for by Barnett consequentials from Boris Johnson’s £1 billion childcare pledge made at the 2019 general election.
Drawing on his own family experiences of a need for childcare, Mr Ross said the policy would "help parents who want to work, but cannot do so because expensive childcare costs do not make it worth their while”.
He said: “With this transformative change to how we deliver funded childcare, we can help to tackle the gender employment gap. Giving opportunity to thousands of Scottish women, who are disproportionately affected, with the promise that they do not have to give up on their job to look after their child.”
Mr Ross admitted the hour extra childcare did “not seem like much”, but he said it could make "the difference between being able to hold down a full-time job or not”. He said the party would “work with youth groups and junior sports clubs” to deliver the new scheme.
Pressed on his pledge to repeal the Hate Crime Bill, Mr Ross said while there were “elements” within it which were needed, “we do have the most controversial piece of legislation ever debated and passed by the Scottish Parliament and we cannot allow that to continue as it is on the statute books”.
He added: “We have a piece of legislation which is completely unfit for purpose overall. We have said there are elements of it which are required and we’ve said all along there are parts needed in Scottish public life, but there was an opportunity for the SNP to work with opposition parties to take out the most damaging parts of the Bill and they refused to do so.
“Therefore we have to repeal this Bill and bring forward the elements that can work, but you cannot do that with a Bill which is so hated and has caused so much controversy within and outwith the Scottish Parliament and it’s a simple fact that only the Scottish Conservatives voted against this ... it’s incredible other opposition parties abetted the SNP to push through this legislation.”
Outlining his plan for Suzanne’s Law, named after Suzanne Pilley, who was murdered in Argyll in 2010, but whose body has never been found, Mr Ross said: “Imagine a loved one being brutally murdered and not even being able to properly say goodbye, how heart-breaking that must be.
“The family are bravely campaigning 11 years later for murderers to be denied parole if they continue to keep their victim’s body hidden.
"We will back their campaign and work in the Scottish Parliament to deliver Suzanne’s Law, building on our plans for a Victims’ Law to place the justice system firmly on the side of victims not the perpetrators of crime.”