From the link to Politifact
But there is no law that mandates separating children from their parents. Trumps own administration devised a policy to that effect.
So what is Trump talking about?
Whenever parents are charged with a federal misdemeanor (entry without inspection in this case), or awaiting trial, they are placed in the custody of the U.S. Marshals Service. Children cannot go to jail, so they are transferred to the custody of Health and Human Services Office of Refugee Resettlement. They are then placed with relatives, juvenile detention centers or foster care. Thats a longstanding Homeland Security policy, DHS told us.
Before the Trump administration, immigrants entering illegally as families were rarely prosecuted, said Sarah Pierce, an associate policy analyst of the U.S. Immigration Program at the Migration Policy Institute. Instead, immigrants were held in family detention centers until they were sent to appear before an immigration court or deported.
The 1997 Flores Settlement Agreement, for example, calls for the release of unaccompanied minors to family members or sponsors who can care for them as their immigration case is resolved. The Trafficking Victims Protection Reauthorization Act of 2008, which Trump has wrongly called "a Democrat rule," determines that unaccompanied minors be transferred to Health and Human Services custody.
http://www.politifact.com/truth-o-meter/statements/2018/may/29/donald-trump/trump-blames-democrat-own-policy-separating-family/