Senator Bernie Sanders’ first executive order as president would be to close America’s private detention facilities, which are part of an ongoing row over the treatment of child migrants, his wife and senior adviser, Jane Sanders, has said.

Jane Sanders was outside a detention facility in Homestead, Florida, along with several 2020 Democratic candidates voicing upset at the immigration policies of Donald Trump.

Jane Sanders told the Guardian it was “heartbreaking” to see the Homestead facility firsthand and outlined what the Vermont senator – who is one of the 2020 frontrunners to take on Trump – would do if he won the White House.

“The first thing – one of the things that he says he’ll do as president – the first executive action he’ll take is to shut these down, to shut down the child detention centers across the country,” she said.

Sanders said her husband has a forthcoming immigration plan informed by Latino staff members and immigrant activists. She also he had voted against legislation that led to the creation of the Immigration and Customs Enforcement (Ice) agency in 2002.

“Everything that he feared has come true,” she said, referring to the agency, “and it needs to be abolished. We need a complete overhaul of our immigration system.”

Homestead, which is run by Comprehensive Health Services, Inc, a private, for-profit company, has become a backdrop for Democratic presidential hopefuls to rail against Trump’s immigration policies while in Miami for the first Democratic debates.

The Massachusetts senator Elizabeth Warren also visited the site and climbed a ladder to peer over a chain-link fence enclosing the detention center for young migrants.

Elizabeth Warren outside the Homestead detention center in Florida, on 26 June. Photograph: Daniel A Varela/AP

Warren said she saw a sprawling campus with massive white tents, metal trailers, a soccer field – and organized in single file lines, the children and young adults who are being housed at Homestead.

“This is not what we should be doing as a country. These children did not commit a crime. These children pose no threat,” Warren said.

“What is happening at Homestead to children – what is happening is the direct result of activities of the United States government is wrong. It is a stain on our country and we must speak out,” she added.

Minnesota senator Amy Klobuchar also arrived on the scene shortly after Warren departed. Democratic hopefuls Beto O’Rourke and author Marianne Williamson are due to visit later this week. The California congressman Eric Swallwell documented his visit on Monday. “These children need homes, NOT a privatized prison,” he said on Twitter.

Their visits come as photos were published of a migrant father and his toddler daughter face down in the Rio Grande river, where they drowned trying to cross the border to seek asylum in the US and amid a fresh found of reports about the inhumane conditions that children are being kept in at border patrol stations near the border.

Lawyers who had visited the facilities said children were being kept without adequate food, water or basic sanitary needs such as toothpaste and soap.