Donald Trump introduced an unorthodox childcare plan Tuesday night, becoming a rare Republican calling for paid maternity leave.

Introduced by his daughter Ivanka, who asserted that childcare issues were at the “root of wage inequality by disproportionately affecting women”, the presidential nominee tried to soften his image in an event held in Delaware County, Pennsylvania, a former stronghold for moderate Republicans that has trended Democratic in recent years.

The proposal came as Trump faces a major deficit among college-educated white women in polls. According to a recent Washington Post/ABC News poll, Hillary Clinton has a 50-40 lead over her Republican rival in a demographic that Mitt Romney won by six points in 2012 despite his decisive loss that year.

Trump called for making a childcare tax deductible, up to the average cost in a given family’s state, until the age of 13, as well as an expanded rebate of up to $1,200 for those families that do not pay income tax and receive earned income tax credit (EITC).

Further, Trump said his plan would provide six weeks of maternity leave “to any mother with a newborn child whose employer does not provide the benefit” by tackling fraud in unemployment insurance. For the six-week period, the mother would receive the equivalent to unemployment benefits while she is out of the workplace. This would not apply to fathers, though.

Trump also strangely asserted that “my opponent has no childcare plan”. Clinton has made a number of detailed proposals on childcare. The Democratic nominee first outlined a program for universal pre-kindergarten in June 2015 and in May 2016 proposed to cap childcare costs at 10% of household income and to introduce 12 weeks of paid family leave.

A woman holds her son as Donald Trump speaks. Photograph: Mike Segar/Reuters

The Clinton campaign held a conference call for reporters on Tuesday to rebut Trump’s plan, which they characterized with audible disdain.

Maya Harris, a senior policy adviser to the former secretary of state, described Trump’s plan as “half-baked and completely out of touch”. In particular, she described the Republican’s proposal for paid maternity leave as “not just regressive, deficient, demeaning and damaging for women” because it only applies to women and pegged to unemployment benefits, not the actual workplace salary of the mother.

Trump’s proposal came the same day as comments from New York attorney general Eric Schneiderman that he had opened an inquiry into the Republican nominee’s personal charity. A source familiar with the matter confirmed to the Guardian that Schneiderman “opened an inquiry on the Trump Foundation based on troubling transactions that have recently come to light”.

Trump also went toe-to-toe with the man he is hoping to replace as Barack Obama made his first solo appearance on the campaign trail on Tuesday. Appearing in downtown Philadelphia, just 20 miles from Trump, the president appeared to coordinate his message with Clinton’s attack on some Trump supporters being “deplorables”.

He told a crowd of thousands: “This isn’t Abraham Lincoln’s Republican party. This isn’t even the vision of freedom that Ronald Reagan talked about.” Instead, he thought the Republican nominee offered “a dark, pessimistic vision of a country where we turn against each other, we turn away from the rest of the world”.

Clinton echoed that message in an attack ad released on Tuesday that used only Trump’s words to paint a picture of the Republican nominee as a candidate who demeaned voters. It was an attempt to repair the damage from the former secretary of state’s statement at a Friday fundraiser that half of Trump’s supporters belonged in the “basket of deplorables”.

Although Clinton quickly backed away from the remark, insisting that she only meant to refer to Trump’s fringe support from the so-called “alt-right”, the Republican nominee has used it as an attack line. Trump insisted in a speech Monday that the remark was “disqualifying” and that Clinton was an elitist for saying it.

The controversy has been compounded by the fact that the former secretary of state has been off the campaign trail for the past few days with pneumonia. Although Clinton was diagnosed on Friday, it wasn’t publicly revealed until Sunday afternoon, eight hours after she had to abruptly leave a ceremony commemorating the September 11 attacks after feeling “overheated”.

The Democratic nominee has had to cancel several days of events, but her campaign told reporters on Tuesday that she would resume travel on Thursday and has announced an event that day in Greensboro, North Carolina.

Clinton’s return to the campaign trail won’t go unchallenged by Trump. The Republican nominee is expected to give a major economic policy address that day at the New York Economic Club.

Sabrina Siddiqui contributed reporting from Philadelphia