A "law to separate families" was enacted prior to April 2018, and the federal government is powerless not to enforce it.

 In mid-June 2018, a number of readers asked about a “law to separate families,” primarily whether the purported legislation was passed by President Barack Obama, President Bill Clinton, or “the Democrats”:

Were children separated from their parents as they crossed the boarder into the USA under the Obama administration?
We are repeatedly informed that the separation of illegal immigrant children from the family is a policy created by the Obama administration. Is this true or is it just Mr. Sessions policy.
Did President Obama’s administration remove children from their parents when they came to the U.S. illegally? Someone on FaceBook is saying this and I want to see if this is true.
NEWSWEEK: OBAMA HELD MORE THAN DOUBLE THE NUMBER OF CHILDREN IN SHELTERS COMPARED TO TRUMP WHITE HOUSE
Did Bill Clinton enact a law that made it legal to separate migrants from their children. We’re migrants forced to surrender their children during the Obama administration?
THE LAW TO SEPARATE PARENTS FROM THEIR CHILDREN WHEN THEY CROSS THE BORDER ILLEGALLY WAS PASSED IN 1997. NOW IT’S A PROBLEM?
Although the questions were varied, their underlying question essentially was the same: Whether a so-called “law to separate parents from children” existed before the Trump administration.  In some versions, President Bill Clinton’s administration passed such a law, and in other iterations, President Barack Obama detained twice as many children separated from their parents during his presidency.
On 5 June 2018, Trump attributed the policy to Democrats in general:
There is no federal law that stipulates that children and parents be separated at the border, no matter how families entered the United States. An increase in child detainees separated from parents stemmed directly from a change in enforcement policy repeatedly announced by Sessions in April and May 2018, under which adults (with or without children) are criminally prosecuted for attempting to enter the United States:
The “zero-tolerance” policy he announced [in May 2018] sees adults who try to cross the border, many planning to seek asylum, being placed in custody and facing criminal prosecution for illegal entry.
As a result, hundreds of minors are now being housed in detention centres, and kept away from their parents.
Over a recent six-week period, nearly 2,000 children were separated from their parents after illegally crossing the border, figures released on [15 June 2018].
[Attorney General] Sessions said those entering the US irregularly would be criminally prosecuted, a change to a long-standing policy of charging most of those crossing for the first time with a misdemeanour offence.
We addressed the “law to separate children” in a fact check about a purported statement made by Attorney General Jeff Sessions. Sessions did not make the statement attributed to him, but he did make a series of remarks in early April 2018 about a new border initiative involving the separation of children from parents at border crossings:
If you are smuggling a child, then we will prosecute you and that child will be separated from you as required by law … If you don’t like that, then don’t smuggle children over our border.
[…]
We don’t want to separate families, but we don’t want families to enter the border illegally[.] We urge them not to do so.
On 7 May 2018, CNN reported that until April 2018, immigration officials used discretion to handle families or unaccompanied minors entering the United States without documentation:
It has long been a misdemeanor federal offense to be caught illegally entering the US, punishable by up to six months in prison, but the administration has not always referred everyone caught for prosecution. Those apprehended were swiftly put into immigration proceedings and, unless they met the threshold to pursue a valid asylum claim, can be quickly deported from the country.
The current DHS plan makes no special arrangements for those who claim asylum when apprehended. While they will be allowed to pursue their claims and could eventually be found to have a legitimate right to live in the US, they could still already have a conviction for illegal entry.
That same article surmised that families “could be” separated, indicating that in the first week of May 2018, the separation of children from families had not yet begun:
The Trump administration has decided to refer every person caught crossing the border illegally for federal prosecution, a policy that could result in the separation of far more parents from their children at the border.
The move would also mean that even if immigrants caught at the border illegally have valid asylum claims, they could still end up with federal criminal convictions on their record regardless of whether a judge eventually finds they have a right to live and stay in the US.
Homeland Security Secretary Kirstjen Nielsen officially enacted the policy on [7 May 2018], according to a Department of Homeland Security official speaking on condition of anonymity. It corresponds with a Department of Justice “zero-tolerance policy” for illegal border crossings, under which Attorney General Jeff Sessions has ordered federal prosecutors to pursue criminal charges against all referrals for illegally crossing the border, as possible.
The rumors correctly suggested that “family detention” as a whole came before the Trump administration, but as of August 2015 intact families at the border were rarely separated. Other iterations of the rumor held that the Obama administration separated more children from their parents than the Trump administration, a claim stemming from an inaccurate retelling of the fact that an influx of unaccompanied minors from Latin America crossed the border in from 2014 onward. In those instances, minor children primarily traveled without their parents. 
Claims that the “law to separate families” was passed in 1997, those claims originated with a February 2018 Department of Homeland Security statement referencing “[l]egal loopholes [that] are exploited by minors, family units, and human smugglers.” The DHS statement claimed existing immigration policies “create a pull factor that invites more illegal immigration and encourages parents to pay and entrust their children to criminal organizations.”
However, neither the 1997 Flores settlement nor a 2008 human trafficking law cited in that release in any way stipulated that the government separate children from their parents:
A White House spokesman referred [Factcheck.org] to a DHS statement regarding a 1997 legal settlement and 2008 antitrafficking law affecting minors who are apprehended without a parent present:
Under the 1997 settlement, DHS could detain unaccompanied children captured at the border for only 20 days before releasing them to foster families, shelters or sponsors, pending resolution of their immigration cases. The settlement was later expanded through other court rulings to include both unaccompanied and accompanied children.
The William Wilberforce Trafficking Victims Protection Reauthorization Act of 2008 requires unaccompanied minors from countries other than Mexico and Canada to be placed in the care of the Office of Refugee Resettlement, or relatives in the U.S., while they go through removal proceedings. The bipartisan bill was approved by unanimous consent and signed by Bush.
But neither the court settlement nor the 2008 law require the Trump administration to “break up families.”
A cluster of rumors about the controversial separation of families at the border held that the policy came before the Trump administration, either stemming from a 1997 “law” or purported policies of previous administrations. Those claims were false. No federal law required or suggested the family separation policy announced by Attorney General Sessions in several sets of remarks during April and May 2018.